Chapter 4 Linear And Quadratic Functions 41 Properties

Ch.4 LinearandQuadraticFunctions

4.1 PropertiesofLinearFunctionsandLinearModels

1 GraphLinearFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinetheslopeandy–interceptofthefunction.

1) f(x)=12x–6

A) m=12;b=–6B)m=12;b=6C)m= –12;b= –6D)m= –12;b=6

2) h(x)=–5x+2

A) m=–5;b=2B)m=5;b= –2C)m=5;b=2D)m= –5;b= –2

3) p(x)=–x+9

A) m=–1;b=9B)m=1;b= – 9C)m= –1;b= – 9D)m=0;b=9

4) f(x)=4

9x–4

A) m=4

9;b=–4B)m=–4;b=4

9C) m=9

4;b=4D)m=–4

9;b=4

5) F(x)=8

A) m=0;b=8B)m=8;b=0C)m=0;b=0D)m=8;b=8

6) G(x)=–3x

A) m=–3;b=0B)m=3;b=0C)m=–1

3;b=0D)m=0;b= –3

7) F(x)=1

4x

A) m=1

4;b=0B)m=4;b=0C)m=–1

4;b=0D)m=0;b=1

4

Page1

Usetheslopeandy–intercepttographthelinearfunction.

8) f(x)=3x–1

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page2

9) g(x)=–3x–2

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page3

10) p(x)=–x+5

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page4

11) f(x)=3

5x+3

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page5

12) h(x)=–3

5x+1

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page6

13) F(x)=2

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page7

14) G(x)=–4x

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page8

15) F(x)=1

4x

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Determinewhetherthegivenfunctionislinearornonlinear.

16)

xy=f(x)

416

624

832

10 40

A) linear B) nonlinear

Page9

2 UseAverageRateofChangetoIdentifyLinearFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinetheaveragerateofchangeforthefunction.

1) f(x)=8x–7

A) 8 B) 7 C) –7D)

–8

2) h(x)=–7x–2

A) –7B)7 C)

–2D)2

3) p(x)=–x–5

A) –1 B) 1 C) 5 D) –5

4) F(x)=–8

A) 0 B) –1

8C) 8 D) –8

5) f(x)=3

5x–2

A) 3

5B) –3

5C) –2D)2

6) h(x)=–1

2x+3

A) –1

2B) 1

2C) 3 D) –3

Page10

3 DetermineWhetheraLinearFunctionIsIncreasing,Decreasing,orConstant

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Graphthefunction.Statewhetheritisincreasing,decreasing,orconstant..

1) f(x)=5x+3

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

A) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page11

2) g(x)=2x–4

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

A) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page12

3) h(x)=–3x+6

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

A) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page13

4) h(x)=–5x–3

A) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page14

5) p(x)=–x+4

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

A) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page15

6) f(x)=2

5x–2

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

A) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page16

7) h(x)=–2

5x–1

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

A) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

B) increasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

C) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

D) decreasing

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

x

-8 -6 -4 -2 2 4 6 8

y

8

6

4

2

-2

-4

-6

-8

Page17

8) F(x)=2

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

A) constant

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

B) constant

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

C) constant

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

x

–8–6–4–2 2468

y

8

6

4

2

-2

-4

-6

-8

D) decreasing

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

4 BuildLinearModelsfromVerbalDescriptions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Supposethatf(x)=–x–3andg(x)=x–12.

(a)Solvef(x)=0.

(b)Solveg(x)=0.

(c)Solvef(x)=g(x).

A) (a)x=–3;(b)x=12;(c)x=4.5 B) (a)x= –3;(b)x=12;(c)x=–7.5

C) (a)x=3;(b)x=12;(c)x=4.5 D) (a)x= –3;(b)x=–12;(c)x=4.5

Page18

2) Supposethatf(x)=–x–9andg(x)=x–18.

(a)Solvef(x)>0.

(b)Solveg(x)>0.

(c)Solvef(x)≤g(x).

A) (a)x

<

–9;(b)x>18;(c)x≥4.5 B) (a)x

<

–9;(b)x

<

18;(c)x≥–13.5

C) (a)x>9;(b)x>18;(c)x>4.5 D) (a)x

<

–9;(b)x

<

–18;(c)x≤4.5

3) Letf(x)bethefunctionrepresentedbythedashedlineandg(x)bethefunctionrepresentedbythesolid

line.Solvetheequationf(x)=g(x).

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) x=3B)x=2C)x= –3D)x= –2

4) Letf(x)bethefunctionrepresentedbythedashedlineandg(x)bethefunctionrepresentedbythesolid

line.Solvetheequationf(x)<g(x).

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) x>3B)x

<

3C)x> –1D)x

<

–1

Page19

5) Letf(x)bethefunctionrepresentedbythedashedlineandg(x)bethefunctionrepresentedbythesolid

line.Solvetheequationf(x)≥g(x).

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

x

–5–4–3–2–1 12345

y

5

4

3

2

1

-1

-2

-3

-4

-5

A) x≤2B)x≥2C)x≥–1D)x

<

–1

6) Atruckrentalcompanyrentsamovingtruckonedaybycharging$31 plus$0.13permile.Writealinear

equationthatrelatesthecostC,indollars,ofrentingthetrucktothenumberxofmilesdriven.Whatisthe

costofrentingthetruckifthetruckisdriven180miles?

A) C(x)=0.13x+31;$54.40 B) C(x)=31x+0.13;$5580.13

C) C(x)=0.13x+31;$33.34 D) C(x)=0.13x–31;–$7.60

7) Lindaneedstohavehercartowed.LittleTownAutochargesaflatfeeof$65 plus$2permiletowed.

WriteafunctionexpressingLindaʹstowingcost,c,intermsofmilestowed,x.Findthecostofhavingacar

towed15miles.

A) c(x)=2x+65;$95 B) c(x)=2x;$30 C) c(x)=2x+65;$85 D) c(x)=2x;$67

8) ToconvertatemperaturefromdegreesCelsiustodegreesFahrenheit,youmultiplythetemperaturei

n

degreesCelsiusby1.8andthenadd32totheresult.ExpressFasalinearfunctionofc.

A) F(c)=1.8c+32 B) F(c)=1.8+32c C) F(c)=33.8c D) F(c)=c–32

1.8

9) Ifanobjectisdroppedoffofatower,thevelocity,V,oftheobjectaftertsecondscanbeobtainedby

multiplyingtby32andadding10totheresult.ExpressVasalinearfunctionoft.

A) V(t)=32t+10 B) V(t)=32+10t C) V(t)=42t D) V(t)=t–10

32

10) Ifanobjectisdroppedfromatower,thenthevelocity,V(infeetpersecond),oftheobjectaftertseconds

canbeobtainedbymultiplyingtby32andadding10totheresult.FindVasalinearfunctionoft,anduse

thisfunctiontoevaluateV(8.9),thevelocityoftheobjectattimet=8.9seconds.

A) V(8.9)=294.8feetpersecond B) V(8.9)=296.1 feetpersecond

C) V(8.9)=294.1feetpersecond D) V(8.9)=292.8 feetpersecond

11) Thecostforlaborassociatedwithfixingawashingmachineiscomputedasfollows:Thereisafixedcharge

of$35fortherepairmantocometothehouse,towhichachargeof$29perhourisadded.Findan

equationthatcanbeusedtodeterminethelaborcost,C(x),ofarepairthattakesxhours.

A) C(x)=35+29x B) C(x)=29 +35x C) C(x)=(35 +29)x D) C(x)=35 –29x

Page20

12) Inacertaincity,thecostofataxirideiscomputedasfollows:Thereisafixedchargeof$2.90 assoonas

yougetinthetaxi,towhichachargeof$2.40permileisadded.Findanequationthatcanbeusedto

determinethecost,C(x),ofanx–miletaxiride.

A) C(x)=2.90+2.40x B) C(x)=2.40 +2.90x C) C(x)=5.30x D) C(x)=3.80x

13) Inacertaincity,thecostofataxirideiscomputedasfollows:Thereisafixedchargeof$2.50 assoonas

yougetinthetaxi,towhichachargeof$1.95permileisadded.Findanequationthatcanbeusedto

determinethecost,C(x),ofanx–miletaxiride,andusethisequationtofindthecostofa2–miletaxiride.

A) $6.40 B) $6.58 C) $6.28 D) $7.30

14) MartyʹsTeeShirt&JacketCompanyistoproduceanewlineofjacketswithanembroideryofaGreat

Pyreneesdogonthefront.Therearefixedcostsof$580tosetupforproduction,andvariablecostsof$31

perjacket.Writeanequationthatcanbeusedtodeterminethetotalcost,C(x),encounteredbyMartyʹs

Companyinproducingxjackets.

A) C(x)=580+31x B) C(x)=580x+31 C) C(x)=(580 +31)x D) C(x)=580 –31x

15) MartyʹsTeeShirt&JacketCompanyistoproduceanewlineofjacketswithaembroideryofaGreat

Pyreneesdogonthefront.Therearefixedcostsof$630tosetupforproduction,andvariablecostsof$39

perjacket.Writeanequationthatcanbeusedtodeterminethetotalcost,C(x),encounteredbyMartyʹs

Companyinproducingxjackets,andusetheequationtofindthetotalcostofproducing88jackets.

A) $4062 B) $4074 C) $4042 D) $4054

16) SupposethatthequantitysuppliedSandquantitydemandedDofbaseballcapsatamajorleaguegame

aregivenbythefunctionsS(p)=4830–100pandD(p)=110p,wherepistheprice.Findtheequilibrium

priceforcapsatthegame.Thenfindtheequilibriumquantity.

A) $23

,

$2530 B) $10

,

$3830 C) $43

,

$530 D) $10

,

$2530

17) Regrind,Inc.regrindsusedtypewriterplatens.Thevariablecostperplatenis$1.40.Thetotalcostto

regrind90platensis$400.Findthelinearcostfunctiontoregrindplatens.Ifregroundplatenssellfor$

10.90each,howmanymustberegroundandsoldtobreakeven?

A) C(x)=1.40x+274;29platens B) C(x)=1.40x+400;43platens

C) C(x)=1.40x+400;33platens D) C(x)=1.40x+274;23platens

18) NorthwestMoldedmoldsplastichandleswhichcost$0.50 perhandletomold.Thefixedcosttorunthe

moldingmachineis$4948perweek.Ifthecompanysellsthehandlesfor$4.50each,howmanyhandles

mustbemoldedandsoldweeklytobreakeven?

A) 1237handles B) 824handles C) 9896 handles D) 989 handles

19) Alumberyardhasfixedcostsof$3933.80 perdayandvariablecostsof$0.14 perboard–footproduced.

Lumbersellsfor$1.44perboard–foot.Howmanyboard–feetmustbeproducedandsolddailytobreak

even?

A) 3026board–feet B) 2017 board–feet C) 28,098 board–feet D) 2489 board–feet

Page21

4.2 BuildingLinearModelsfromData

1 DrawandInterpretScatterDiagrams

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Plotascatterdiagram.

1) x16 –13 14 –13 –213 223 4–6

y62 28 40 –8–336 968 –84

x

-100 -50 50 100

y

50

-50

x

-100 -50 50 100

y

50

-50

A)

x

-100 -50 50 100

y

100

50

-50

-100

x

-100 -50 50 100

y

100

50

-50

-100

B)

x

-100 -50 50 100

y

100

50

-50

-100

x

-100 -50 50 100

y

100

50

-50

-100

C)

x

-100 -50 50 100

y

100

50

-50

-100

x

-100 -50 50 100

y

100

50

-50

-100

D)

x

-100 -50 50 100

y

100

50

-50

-100

x

-100 -50 50 100

y

100

50

-50

-100

Page22

2)

x19 23 31 50 57 61 76 81 92

y142537496746689382

x

-100 -50 50 100

y

100

50

-50

-100

x

-100 -50 50 100

y

100

50

-50

-100

A)

x

-100 -50 50 100

y

100

50

-50

-100

x

-100 -50 50 100

y

100

50

-50

-100

B)

x

-100 -50 50 100

y

100

50

-50

-100

x

-100 -50 50 100

y

100

50

-50

-100

C)

x

–100 -50 50 100

y

100

50

-50

–100

x

–100 -50 50 100

y

100

50

-50

–100

D)

x

–100 -50 50 100

y

100

50

-50

–100

x

–100 -50 50 100

y

100

50

-50

–100

3) Drawascatterdiagramofthegivendata.Findtheequationofthelinecontainingthepoints(1

,

1.3)and

(9,4.3).Graphthelineonthescatterdiagram.

x13689

y1.3 2.1 3.0 3.4 4.3

Page23

x

246810

y

5

4

3

2

1

x

246810

y

5

4

3

2

1

A) y=0.38x+0.93

x

246810

y

5

4

3

2

1

x

246810

y

5

4

3

2

1

B) y=0.3x+1

x

246810

y

5

4

3

2

1

x

246810

y

5

4

3

2

1

C) y=0.41x+0.93

x

246810

y

5

4

3

2

1

x

246810

y

5

4

3

2

1

D) y=0.36x+0.9

x

246810

y

5

4

3

2

1

x

246810

y

5

4

3

2

1

4) Drawascatterdiagramofthegivendata.Findtheequationofthelinecontainingthepoints(2.0

,

8.3) and

(4.6,2.9).Graphthelineonthescatterdiagram.

x1.2 2.0 2.8 3.8 4.6

y9.3 8.3 5.9 4.6 2.9

Page24

x

12345

y

14

12

10

8

6

4

2

x

12345

y

14

12

10

8

6

4

2

A) y=–2.08x+12.45

x

12345

y

14

12

10

8

6

4

2

x

12345

y

14

12

10

8

6

4

2

B) y= –1.67x+10.57

x

12345

y

14

12

10

8

6

4

2

x

12345

y

14

12

10

8

6

4

2

C) y=2.08x+12.45

x

12345

y

14

12

10

8

6

4

2

x

12345

y

14

12

10

8

6

4

2

D) y= –2.28x+12.95

x

12345

y

14

12

10

8

6

4

2

x

12345

y

14

12

10

8

6

4

2

Plotandinterprettheappropriatescatterdiagram.

5) ThetablegivesthetimesspentwatchingTVandthegradesofseveralstudents.

WeeklyTV(h)6 1218243036

Grade(%) 92.5 87.5 72.5 77.5 62.5 57.5

EffectofWatchingTVonGrades

Page25

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

A) EffectofWatchingTVonGrades

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

MorehoursspentwatchingTVmay

reducegrades.

B) EffectofWatchingTVonGrades

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

MorehoursspentwatchingTVmay

increasegrades.

C) EffectofWatchingTVonGrades

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

MorehoursspentwatchingTVmay

reducegrades.

D) EffectofWatchingTVonGrades

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

6 1218243036

100

90

80

70

60

50

40

30

20

10

Weekly TV (hr)

Grade (%)

MorehoursspentwatchingTVmay

increasegrades.

6) Thetableshowsthestudytimesandtestscoresforanumberofstudents.Drawascatterplotofscore

versustimetreatingtimeastheindependentvariable.

StudyTime(min) 9 16 21 26 33 36 40 47

TestScore 59 61 64 65 73 74 78 78

EffectofStudyonTestScore

Page26

10 20 30 40 50

80

70

60

50

Test Score

10 20 30 40 50

80

70

60

50

Test Score

Time(min)

A) EffectofStudyonTestScore

10 20 30 40 50

80

70

60

50

Test Score

10 20 30 40 50

80

70

60

50

Test Score

Time(min)

Moretimespentstudyingmayincrease

testscores.

B) EffectofStudyonTestScore

10 20 30 40 50

80

70

60

50

Test Score

10 20 30 40 50

80

70

60

50

Test Score

Time(min)

Moretimespentstudyingmaydecrease

testscores.

C) EffectofStudyonTestScore

10 20 30 40 50

80

70

60

50

Test Score

10 20 30 40 50

80

70

60

50

Test Score

Time(min)

Moretimespentstudyingmaydecrease

testscores.

D) EffectofStudyonTestScore

10 20 30 40 50

80

70

60

50

Test Score

10 20 30 40 50

80

70

60

50

Test Score

Time(min)

Moretimespentstudyingmayincrease

testscores.

Page27

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

7) Theone–daytemperaturesfor12worldcitiesalongwiththeirlatitudesareshowninthetablebelow.

Makeascatterdiagramforthedata.Describewhathappenstotheone–daytemperaturesasthelatitude

increases.

City Temperature(F) Latitude

Oslo,Norway

Seattle,WA

Anchorage,AK

Paris,France

Vancouver,Canada

London,England

Tokyo,Japan

Cairo,Egypt

MexicoCity,Mexico

Miami,FL

NewDelhi,India

Manila,Philippines

30°

57°

40°

61°

54°

48°

55°

82°

84°

81°

95°

93°

59°

47°

61°

48°

49°

51°

35°

30°

19°

25°

28°

14°

Latitude(degrees)

x

10 20 30 40 50 60 70 80 90

y

100

90

80

70

60

50

40

30

20

10

x

10 20 30 40 50 60 70 80 90

y

100

90

80

70

60

50

40

30

20

10

Temperature(F)°

Page28

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

8) Thefollowingscatterdiagramshowsheights(ininches)ofchildrenandtheirages.

Height(inches)

x

123456789101112131415

y

72

66

60

54

48

42

36

30

24

18

12

6

x

123456789101112131415

y

72

66

60

54

48

42

36

30

24

18

12

6

Age(years)

Whathappenstoheightasageincreases?

A) Heightincreasesasageincreases. B) Heightdecreasesasageincreases.

C) Heightstaysthesameasageincreases. D) Heightandagedonotappeartoberelated.

9) Thefollowingscatterdiagramshowsheights(ininches)ofchildrenandtheirages.

Height(inches)

123456789

50

45

40

35

30

25

20

15

10

5

123456789

50

45

40

35

30

25

20

15

10

5

Age(years)

Whatistheexpectedheightrangefora2–yearoldchild?

A) 25–38inches B) 20–30inches C) 40–50inches D) 35–45inches

Page29

10) Thefollowingscatterdiagramshowsheights(ininches)ofchildrenandtheirages.

Height(inches)

123456789

50

45

40

35

30

25

20

15

10

5

123456789

50

45

40

35

30

25

20

15

10

5

Age(years)

Basedonthisdata,howolddoyouthinkachildiswhoisabout39inchestall?

A) 3years B) 3months C) 1year D) 7years

Page30

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

11) Thefollowingdatarepresentstheheight(ininches)andweight(inpounds)of9randomlyselectedadults.



Height,x(in.) Weight,y(lb)

65 142

72 189

61 111

68 158

74 196

66 170

62 126

70 180

67 183

Graphthedataonascatterdiagramtreatingheightastheindependentvariable.Findanequationofthe

linecontainingthepoints(62,126)and(70,180).Expresstherelationshipusingfunctionnotation.Graph

thelineonthescatterdiagram.Interprettheslopeoftheline.Usethelinetopredicttheweightofaperson

whois61.6inchestall.Roundtothenearestpound.

x

60 62 64 66 68 70 72 74 76

y

200

180

160

140

120

100

Weight (lb)

x

60 62 64 66 68 70 72 74 76

y

200

180

160

140

120

100

Weight (lb)

Height(inches)

Page31

12) Ultravioletradiationfromthesunisthoughttobeonefactorcausingskincancer.TheamountofUV

radiationapersonreceivesisafunctionofthethicknessoftheearthʹsozonelayerwhichdependsonthe

latitudeoftheareawherethepersonlives.Thefollowingdatarepresentthelatitudesandmelanomarates

forninerandomlyselectedareasintheUnitedStates.Themelanomaratesrefertoathree–yearperiod.

DegreesNorth

Latitude,x

MelanomaRate

(per100,000),y

32.4 7.1

33.7 6.9

34.4 6.3

36.5 5.4

38.1 4.8

39.9 4.4

41.6 4.1

43.2 3.3

44.0 3.0

Graphthedataonascatterdiagramtreatinglatitudeastheindependentvariable.Findanequationofthe

linecontainingthepoints(32.4,7.1)and(43.2,3.3).Expresstherelationshipusingfunctionnotation.Graph

thelineonthescatterdiagram.Interprettheslopeoftheline.Usethelinetopredictthemelanomarateof

anareawithalatitudeof36.7degreesnorth.

x

30 32 34 36 38 40 42 44 46

y

9

8

7

6

5

4

3

2

1

Latitude (degrees north)

Melanoma Rate (per 100,000)

x

30 32 34 36 38 40 42 44 46

y

9

8

7

6

5

4

3

2

1

Latitude (degrees north)

Melanoma Rate (per 100,000)

Page32

2 DistinguishbetweenLinearandNonlinearRelations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determineifthetypeofrelationislinear,nonlinear,ornone.

1)

A) linear B) nonlinear C) none

2)

A) linear B) nonlinear C) none

3)

A) nonlinear B) linear C) none

Page33

4)

A) nonlinear B) linear C) none

5)

A) nonlinear B) linear C) none

6)

A) none B) linear C) nonlinear

Page34

Solvetheproblem.

7) Identifythescatterdiagramoftherelationthatappearslinear.

A) B)

C) D)

3 UseaGraphingUtilitytoFindtheLineofBestFit

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Useagraphingutilitytofindtheequationofthelineofbestfit.Roundtotwodecimalplaces,ifnecessary.

1) x2456

y711 13 20

A) y=3x B) y=2.8x+0.15 C) y=2.8x D) y=3x+0.15

2) x6820 28 36

y2413 20 30

A) y=0.90x–3.79 B) y=0.95x–2.79 C) y=0.80x–3.79 D) y=0.85x–2.79

3) x13579

y143 116 100 98 90

A) y=–6.2x+140.4 B) y=6.2x–140.4 C) y= –6.8x+150.7 D) y=6.8x–150.7

4) x123456

y17 20 19 22 21 24

A) y=1.17x+16.4 B) y=1.03x+18.9 C) y=1.17x+18.9 D) y=1.03x+16.4

Page35

5) x034512

y826912

A) y=0.53x+4.88 B) y=0.43x+4.98 C) y=0.63x+4.88 D) y=0.73x+4.98

6) x35715 16

y811 714 20

A) y=0.75x+5.07 B) y=0.75x+4.07 C) y=0.85x+3.07 D) y=0.95x+3.07

7) x24 26 28 30 32

y15 13 20 16 24

A) y=1.05x–11.8 B) y=1.05x+11.8 C) y=0.95x–11.8 D) y=0.95x+11.8

8) x246810

y15 37 60 75 94

A) y=9.8x–2.6 B) y=10x–3C)y=9.2x–2.1 D) y=9x–3

9) x1.2 1.4 1.6 1.8 2.0

y54 53 55 54 56

A) y=2.5x+50.4 B) y=54 C) y=3x+50 D) y=55.3

10) x10 20 30 40 50

y3.9 4.6 5.4 6.9 8.3

A) y=0.11x+2.49 B) y=x–8C)y=0.5x–2D)y=0.17x+2.11

11) x237810

y3445 6

A) y=0.30x+4.29 B) y=0.30x+2.57 C) y=0.32x+4.29 D) y=0.32x+2.57

12) x237810

y2446 6

A) y=0.43x+1.79 B) y=1.79x–1.86 C) y=1.79x+0.43 D) y= –1.86x+1.79

13) Tenstudentsinagraduateprogramwererandomlyselected.Theirgradepointaverages(GPAs)when

theyenteredtheprogramwerebetween3.5and4.0.Thefollowingdatawereobtainedregardingtheir

GPAsonenteringtheprogramversustheircurrentGPAs.

EnteringGPA CurrentGPA

3.5 3.6

3.8 3.7

3.6 3.9

3.6 3.6

3.5 3.9

3.9 3.8

4.0 3.7

3.9 3.9

3.5 3.8

3.7 4.0

A) y=0.03x+3.67 B) y=0.02x+4.91 C) y=0.50x+5.81 D) y=0.33x+2.51

Page36

14) Twodifferenttestsaredesignedtomeasureemployeeproductivityanddexterity.Severalemployeesare

randomlyselectedandtestedwiththeseresults.

Productivity

Dexterity

23 25 28 21 21 25 26 30 34 36

49 53 59 42 47 53 55 63 67 75

A) y=5.05+1.91x B) y=2.36+2.03x C) y=10.7+1.53x D) y=75.3–0.329x

15) Managersrateemployeesaccordingtojobperformanceandattitude.Theresultsforseveralrandomly

selectedemployeesaregivenbelow.

Performance

Attitude

59 63 65 69 58 77 76 69 70 64

72 67 78 82 75 87 92 83 87 78

A) y=11.7+1.02x B) y=2.81+1.35x C) y= –47.3+2.02x D) y=92.3–0.669x

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Solvetheproblem.

16) Theone–daytemperaturesfor12worldcitiesalongwiththeirlatitudesareshowninthetablebelow.

Makeascatterdiagramforthedata.Thenfindthelineofbestfitandgraphitonthescatterdiagram.

City Temperature(F) Latitude

Oslo,Norway

Seattle,WA

Anchorage,AK

Paris,France

Vancouver,Canada

London,England

Tokyo,Japan

Cairo,Egypt

MexicoCity,Mexico

Miami,FL

NewDelhi,India

Manila,Philippines

30°

57°

40°

61°

54°

48°

55°

82°

84°

81°

95°

93°

59°

47°

61°

48°

49°

51°

35°

30°

19°

25°

28°

14°

Latitude(degrees)

x

10 20 30 40 50 60 70 80 90

y

100

90

80

70

60

50

40

30

20

10

x

10 20 30 40 50 60 70 80 90

y

100

90

80

70

60

50

40

30

20

10

Temperature(F)°

Page37

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

17) Adrugcompanyestablishesthatthemosteffectivedoseofanewdrugrelatestobodyweightasshown

below.Letbodyweightbetheindependentvariableanddrugdosagebethedependentvariable.Usea

graphingutilitytodrawascatterdiagramandtofindthelineofbestfit.Whatisthemosteffectivedosage

forapersonweighing110lbs?

Body

Weight(lbs)

Drug

Dosage(mg)

50 10

100 13

150 15

200 17

250 19

A) 13.04mg B) 28.66 mg C) 14 mg D) 13.07 mg

18) Amarinaownerwishestoestimatealinearfunctionthatrelatesboatlengthinfeetanditsdraft(deptho

f

boatbelowwaterline)infeet.Hecollectsthefollowingdata.Letboatlengthrepresenttheindependent

variableanddraftrepresentthedependentvariable.Useagraphingutilitytodrawascatterdiagramand

tofindthelineofbestfit.Whatisthedraftforaboat60ftinlength(tothenearesttenth)?

BoatLength(ft) Draft(ft)

25 2.5

25 2

30 3

30 3.5

45 6

45 7

50 7

50 8

A) 9.7 B) 15.7 C) 10.5 D) 10.3

19) AsurveyoftheinterestratesearnedbyCertificatesofDeposit(CDs)showedthefollowingpercentsfor

thelengthoftime(inyears)forholdingtheCD.Letlengthoftimerepresenttheindependentvariableand

interestraterepresentthedependentvariable.Useagraphingutilitytodrawascatterdiagramandtofind

thelineofbestfit.WhatistheestimateoftheinterestrateforaCDheldfor30years(tothenearest

thousandth)?

CDMaturity(yrs) Interestrate(%)

58.458

10 8.470

15 8.496

20 8.580

25 8.625

A) 8.669 B) 8.675 C) 9.064 D) 8.874

Page38

20) SuperSally,atrulyamazingindividual,picksuparockandthrowsitashardasshecan.Thetablebelow

displaystherelationshipbetweentherockʹshorizontaldistance,d(infeet)fromSallyandtheinitialspeed

withwhichshethrows.

Initialspeed(inft/sec),v1015 20 25 30

Horizontaldistanceoftherock(infeet),d 9.9 14.8 19.1 24.5 28.2

Assumethatthehorizontaldistancetravelledvarieslinearlywiththespeedwithwhichtherockis

thrown.Usingagraphingutility,findthelineofbestfit,andestimate,roundedtotwodecimalplaces,the

horizontaldistanceoftherockiftheinitialspeedis33ft/sec.

A) 31.34feet B) 26.67feet C) 34.76feet D) 31.33feet

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

21) ThefollowingdatarepresentstheamountofmoneyTomissavingeachmonthsincehegraduatedfrom

college.

month 1234 5 6 7

savings $52 $70 $81 $91 $102 $118 $132

Usingthelineofbestfitforthedataset,predicttheamounthewillsaveinthe24thmonthafter

graduatingfromcollege.

22) ThefollowingdatarepresentstheamountofmoneyTomissavingeachmonthsincehegraduatedfrom

college.

month 1234 5 6 7

savings $52 $70 $81 $91 $102 $118 $132

Findtheslopeofthelineofbestfitforthedatasetandinterpretit.

23) ThefollowingdatarepresentstheOlympicwinningtimeinWomenʹs100mFreestyle.

year 1972 1976 1980 1984 1988 1992 1996

time 58.59 55.65 54.79 55.92 54.93 54.65 54.50

Usingthelineofbestfit(withslopecorrectto5decimalplaces)forthedataset,predicttheOlympic

winningtimein2000.

24) ThefollowingdatarepresentstheOlympicwinningtimeinWomenʹs100mFreestyle.

year 1972 1976 1980 1984 1988 1992 1996

time 58.59 55.65 54.79 55.92 54.93 54.65 54.50

Findtheslopeofthelineofbestfitforthedatasetandinterpretit.

Page39

25) Thefollowingdatarepresentsthenumberofemployeesatacompanyatthestartofeachyearsincethe

companybegan.

month 1 2345 6 7

number 3 172 403 571 823 1061 1194

Usingthelineofbestfitforthedataset,predictthenumberofemployeesatthestartofthe10thyear.

26) Thefollowingdatarepresentsthenumberofemployeesatacompanyatthestartofeachyearsincethe

companybegan.

month 1 2345 6 7

number 3 172 403 571 823 1061 1194

Findtheslopeofthelineofbestfitforthedatasetandinterpretit.

4.3 QuadraticFunctionsandTheirProperties

1 GraphaQuadraticFunctionUsingTransformations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Matchthegraphtooneofthelistedfunctions.

1)

x

-2 2

y

2

-2

x

-2 2

y

2

-2

A) f(x)=x2–2xB) f(x)=x2+2xC) f(x)=x2–2x–1 D) f(x)=x2+2x–1

2)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A) f(x)=–x2–10x B) f(x)=x2–10x C) f(x)=–x2–10 D) f(x)=x2–10

Page40

3)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A) f(x)=–x2–12 B) f(x)=x2–12x C) f(x)=–x2–12x D) f(x)=x2–12

4)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A) f(x)=x2–2 B) f(x)=x2–2x C) f(x)=–x2–2x D) f(x)=–x2–2

Graphthefunctionfbystartingwiththegraphofy=x2andusingtransformations(shifting,compressing,

stretching,and/orreflection).

5) f(x)=x2–2

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page41

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page42

6) f(x)=–2x2

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page43

7) f(x)=1

3x2

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page44

8) f(x)=1

2x2+5

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page45

9) f(x)=–2x2–5

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page46

10) f(x)=2x2–1

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page47

11) f(x)=–x2–4x

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

B)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

C)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

D)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

12) f(x)=x2+8x+7

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page48

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page49

13) f(x)=–6x2+12x+4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page50

14) f(x)=5

4x2+5

2x–1

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page51

15) f(x)=–x2+8x–13

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

2 IdentifytheVertexandAxisofSymmetryofaQuadraticFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findthevertexandaxisofsymmetryofthegraphofthefunction.

1) f(x)=x2+6x

A) (–3

,

–9);x=–3B)(

–9

,

3);x= –9C)(3

,

–9);x=3D)(9

,

–3);x=9

2) f(x)=x2–10x

A) (5

,

–25);x=5B)(

–25

,

5);x= –25 C) (–5

,

25);x= –5D)(25

,

–5);x=25

Page52

3) f(x)=–x2+8x

A) (4

,

16);x=4B)(

–16

,

4);x= –16 C) (–4

,

–16);x= –4D)(16

,

–4);x=16

4) f(x)=–x2–4x

A) (–2

,

4);x=–2B)(

–4

,

2);x= –4C)(2

,

–4);x=2D)(4

,

–2);x=4

5) f(x)=–2x2+16x

A) (4

,

32);x=4B)(

–4

,

32);x= –4C)(4

,

0);x=4D)(

–4

,

0);x= –4

6) f(x)=x2+2x–3

A) (–1

,

–4);x=–1B)(1

,

–4);x=1C)(1

,

4);x=1D)(

–1

,

4);x= –1

7) f(x)=–x2+4x+9

A) (2

,

13);x=2B)(

–2

,

–3);x= –2C)(4

,

9);x=4D)(

–2

,

5);x= –2

8) f(x)=–2x2+4x+5

A) (1

,

7);x=1B)(

–1

,

–1);x= –1C)(2

,

1);x=2D)(

–2

,

–11);x= –2

9) f(x)=x2+3x–6

A) –3

2,–33

4

;x=–3

2B) 3

2,3

4

;x=3

2

C) (–1

,

–6);x=–1D)(3

,

12);x=3

10) f(x)=–4x2–2x–6

A) –1

4,–23

4;x=–1

4B) (4

,

–6);x=4

C) 1

4,23

4;x=1

4D) –4,–23

4;x=–4

Page53

3 GraphaQuadraticFunctionUsingItsVertex,Axis,andIntercepts

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Graphthefunctionusingitsvertex,axisofsymmetry,andintercepts.

1) f(x)=x2+4x

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A) vertex(–2

,

–4)

intercepts(0,0),(–4,0)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

B) vertex(2

,

–4)

intercepts(0,0),(4,0)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

C) vertex(2

,

4)

intercept(0,8)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

D) vertex(–2

,

4)

intercept(0,8)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

Page54

2) f(x)=–x2+4x

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A) vertex(2

,

4)

intercepts(0,0),(4,0)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

B) vertex(2

,

–4)

intercept(0,–8)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

C) vertex(–2

,

4)

intercepts(0,0),(–4,0)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

D) vertex(–2

,

–4)

intercept(0,–8)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

Page55

3) f(x)=x2+2x+1

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

A) vertex(–1

,

0)

intercepts(0,1),(–1,0)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

B) vertex(1

,

0)

intercepts(0,1),(1,0)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

C) vertex(1

,

1)

intercept(0,2)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

D) vertex(–1

,

1)

intercept(0,2)

x

-10 -5 5 10

y

40

20

-20

-40

x

-10 -5 5 10

y

40

20

-20

-40

Page56

4) f(x)=x2+2x–3

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) vertex(–1

,

–4)

intercepts(1,0),(–3,0),(0,–3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) vertex(1

,

–4)

intercepts(–1,0),(3,0),(0,–3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) vertex(1

,

4)

intercepts(–1,0),(3,0),(0,3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) vertex(–1

,

4)

intercepts(1,0),(–3,0),(0,3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page57

5) f(x)=–x2–6x–5

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) vertex(–3

,

4)

intercepts(–1,0),(–5,0),(0,–5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) vertex(3

,

–4)

intercepts(1,0),(5,0),(0,5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) vertex(3

,

4)

intercepts(1,0),(5,0),(0,–5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) vertex(–3

,

–4)

intercepts(–1,0),(–5,0),(0,5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page58

6) f(x)=x2–8x+7

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) vertex(4

,

–9)

intercepts(7,0),(1,0),(0,7)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) vertex(–4

,

–9)

intercepts(–7,0),(–1,0),(0,7)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) vertex(–4

,

9)

intercepts(–7,0),(–1,0),(0,–7)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) vertex(4

,

9)

intercepts(7,0),(1,0),(0,–7)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page59

7) f(x)=–x2+6x–5

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) vertex(3

,

4)

intercepts(5,0),(1,0),(0,–5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) vertex(–3

,

–4)

intercepts(–5,0),(–1,0),(0,5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) vertex(–3

,

4)

intercepts(–5,0),(–1,0),(0,–5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) vertex(3

,

–4)

intercepts(5,0),(1,0),(0,5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page60

8) f(x)=–4x2–16x–19

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) vertex(–2

,

–3)

intercept(0,–19)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B) vertex(2

,

–3)

intercept(0,–19)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C) vertex(–2

,

–3)

intercept0,–4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D) vertex(2

,

–3)

intercept0,–4

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page61

9) f(x)=–8x2–2x–3

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

x

–10–8-6-4-2 2 4 6 810

y

10

8

6

4

2

-2

-4

-6

-8

-10

A) vertex–1

8,–23

8

intercept(0,–3)

x

–5–4–3–2–1 12345

y

25

20

15

10

5

-5

-10

-15

-20

-25

x

–5–4–3–2–1 12345

y

25

20

15

10

5

-5

-10

-15

-20

-25

B) vertex–1

8,23

8

intercept(0,3)

x

-5 -4 -3 -2 –1 1 2 3 4 5

y

25

20

15

10

5

-5

-10

-15

-20

-25

x

-5 -4 -3 -2 –1 1 2 3 4 5

y

25

20

15

10

5

-5

-10

-15

-20

-25

C) vertex1

8,–23

8

intercept(0,–3)

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

25

20

15

10

5

-5

-10

-15

-20

-25

x

-5 -4 -3 -2 -1 1 2 3 4 5

y

25

20

15

10

5

-5

-10

-15

-20

-25

D) vertex1

8,23

8

intercept(0,3)

x

-5 -4 -3 -2 –1 1 2 3 4 5

y

25

20

15

10

5

-5

-10

-15

-20

-25

x

-5 -4 -3 -2 –1 1 2 3 4 5

y

25

20

15

10

5

-5

-10

-15

-20

-25

Page62

Determinethedomainandtherangeofthefunction.

10) f(x)=x2–12x

A) domain:allrealnumbers

range:{y|y≥–36}

B) domain:{x|x≥6}

range:{y|y≥–36}

C) domain:{x|x≥–6}

range:{y|y≥36}

D) domain:allrealnumbers

range:{y|y≥36}

11) f(x)=–x2+10x

A) domain:allrealnumbers

range:{y|y≤25}

B) domain:{x|x≤5}

range:{y|y≤25}

C) domain:{x|x≤–5}

range:{y|y≤25}

D) domain:allrealnumbers

range:{y|y≤–25}

12) f(x)=x2+8x+16

A) domain:allrealnumbers

range:{y|y≥0}

B) domain:{x|x≥–4}

range:{y|y≥0}

C) domain:{x|x≥4}

range:{y|y≥0}

D) domain:allrealnumbers

range:{y|y≥16}

13) f(x)=x2+2x–8

A) domain:allrealnumbers

range:{y|y≥–9}

B) domain:range:{x|x≥1}

range:{y|y≥–9}

C) domain:range:{x|x≥1}

range:{y|y≥9}

D) domain:allrealnumbers

range:{y|y≥9}

14) f(x)=–x2–8x–7

A) domain:allrealnumbers

range:{y|y≤9}

B) domain:{x|x≤–4}

range:{y|y≤9}

C) domain:{x|x≤–4}

range:{y|y≤–9}

D) domain:allrealnumbers

range:{y|y≤–9}

15) f(x)=x2–4x–5

A) domain:allrealnumbers

range:{y|y≥–9}

B) domain:{x|x≥–2}

range:{y|y≥–9}

C) domain:allrealnumbers

range:{y|y≤9}

D) domain:allrealnumbers

range:allrealnumbers

16) f(x)=–x2+6x–8

A) domain:allrealnumbers

range:{y|y≤1}

B) domain:{x|x≤–3}

range:{y|y≤1}

C) domain:allrealnumbers

range:{y|y≤–1}

D) domain:allrealnumbers

range:allrealnumbers

17) f(x)=–11x2–2x–6

A) domain:allrealnumbers

range:yy≤–65

11

B) domain:allrealnumbers

range:yy≥–65

11

C) domain:allrealnumbers

range:yy≥65

11

D) domain:allrealnumbers

range:yy≤65

11

Page63

Determinewherethefunctionisincreasingandwhereitisdecreasing.

18) f(x)=x2–6x

A) increasingon(3

,

∞)

decreasingon(–∞,3)

B) increasingon(–∞

,

3)

decreasingon(3,∞)

C) increasingon(–∞

,

–3)

decreasingon(–3,∞)

D) increasingon(–3

,

∞)

decreasingon(–∞,–3)

19) f(x)=–x2+8x

A) increasingon(–∞

,

4)

decreasingon(4,∞)

B) increasingon(4

,

∞)

decreasingon(–∞,4)

C) increasingon(–4

,

∞)

decreasingon(–∞,–4)

D) increasingon(–∞

,

–4)

decreasingon(–4,∞)

20) f(x)=x2–10x+25

A) increasingon(5

,

∞)

decreasingon(–∞,5)

B) increasingon(–∞

,

5)

decreasingon(5,∞)

C) increasingon(–∞

,

–5)

decreasingon(–5,∞)

D) increasingon(–5

,

∞)

decreasingon(–∞,–5)

21) f(x)=x2+6x+5

A) increasingon(–3

,

∞)

decreasingon(–∞,–3)

B) increasingon(–∞

,

–3)

decreasingon(–3,∞)

C) increasingon(–4

,

∞)

decreasingon(–∞,–4)

D) increasingon(–∞

,

–4)

decreasingon(–4,∞)

22) f(x)=–x2–4x–3

A) increasingon(–∞

,

–2)

decreasingon(–2,∞)

B) increasingon(–2

,

∞)

decreasingon(–∞,–2)

C) increasingon(–∞

,

1)

decreasingon(1,∞)

D) increasingon(1

,

∞)

decreasingon(–∞,1)

23) f(x)=x2–8x+7

A) increasingon(4

,

∞)

decreasingon(–∞,4)

B) increasingon(–∞

,

4)

decreasingon(4,∞)

C) increasingon(–∞

,

–9)

decreasingon(–9,∞)

D) increasingon(–9

,

∞)

decreasingon(–∞,–9)

24) f(x)=–x2+4x–3

A) increasingon(–∞

,

2)

decreasingon(2,∞)

B) increasingon(2

,

∞)

decreasingon(–∞,2)

C) increasingon(1

,

∞)

decreasingon(–∞,1)

D) increasingon(–∞

,

1)

decreasingon(1,∞)

25) g(x)=7x2+56x+63

A) decreasingon(–∞

,

–4)

increasingon(–4,∞)

B) increasingon(–∞

,

–28)

decreasingon(–28,∞)

C) decreasingon(–∞

,

4)

increasingon(4,∞)

D) increasingon(–∞

,

–4)

decreasingon(–4,∞)

Page64

26) f(x)=–8x2–2x–9

A) increasingon–∞,–1

8

decreasingon–1

8,∞

B) decreasingon–∞,–1

8

increasingon–1

8,∞

C) increasingon–∞,1

8

decreasingon1

8,∞

D) increasingon–∞,–71

8

decreasingon–71

8,∞

4 FindaQuadraticFunctionGivenItsVertexandOneOtherPoint

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determinethequadraticfunctionwhosegraphisgiven.

1)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Vertex:(–1,4)

y–intercept:(0,3)

A) f(x)=–x2–2x+3 B) f(x)=–x2–2x–3 C) f(x)=x2–4x+3 D) f(x)=–x2–4x+3

2)

x

-5 5

y

5

-5

(2, –2)

(0, 2)

x

-5 5

y

5

-5

(2, –2)

(0, 2)

A) f(x)=x2–4x+2 B) f(x)=–x2+4x–2 C) f(x)=x2+8x+2 D) f(x)=–x2–4x+2

Page65

5 FindtheMaximumorMinimumValueofaQuadraticFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Determine,withoutgraphing,whetherthegivenquadraticfunctionhasamaximumvalueoraminimumvalueand

thenfindthatvalue.

1) f(x)=x2+1

A) minimum;1 B) minimum;0 C) maximum;0 D) maximum;1

2) f(x)=x2–8

A) minimum;–8 B) minimum;0 C) maximum;–8 D) maximum;0

3) f(x)=x2–2x–9

A) minimum;–10 B) maximum;–10 C) minimum;1 D) maximum;1

4) f(x)=–x2+2x–4

A) maximum;–3 B) minimum;–3 C) minimum;1 D) maximum;1

5) f(x)=4x2–2x–3

A) minimum;–13

4B) maximum;–13

4C) minimum; 1

4D) maximum; 1

4

6) f(x)=5x2+15x

A) minimum;–45

4B) maximum;–45

4C) minimum;–3

2D) maximum;–3

2

7) f(x)=–5x2–10x

A) maximum;5 B) minimum;5 C) minimum;–5 D) maximum;–5

8) f(x)=–9x2–2x–4

A) maximum;–35

9B) minimum;–35

9C) maximum; 35

9D) minimum; 35

9

Solvetheproblem.

9) ThemanufacturerofaCDplayerhasfoundthattherevenueR(indollars)is

R(p)=–5p2+1560p,whentheunitpriceispdollars.Ifthemanufacturersetsthepriceptomaximize

revenue,whatisthemaximumrevenuetothenearestwholedollar?

A) $121,680 B) $243,360 C) $486,720 D) $973,440

10) TheownerofavideostorehasdeterminedthatthecostC,indollars,ofoperatingthestoreis

approximatelygivenbyC(x)=2x2–20x+600,wherexisthenumberofvideosrenteddaily.Findthe

lowestcosttothenearestdollar.

A) $550 B) $400 C) $500 D) $650

11) Thepricepandthequantityxsoldofacertainproductobeythedemandequation

p=–1

7x+180,0≤x≤1260.

Whatquantityxmaximizesrevenue?Whatisthemaximumrevenue?

A) 630;$56,700 B) 315;$42,525 C) 945;$42,525 D) 1260;$56,700

Page66

12) Thepricepandthequantityxsoldofacertainproductobeythedemandequation

p=–1

2x+180,0≤x≤360.

Whatpriceshouldthecompanychargetomaximizerevenue?

A) $90 B) $108 C) $135 D) $45

13) Thepricep(indollars)andthequantityxsoldofacertainproductobeythedemandequation

x=–9p+252,0≤p≤28.

Whatquantityxmaximizesrevenue?Whatisthemaximumrevenue?

A) 126;$1764 B) 63;$1323 C) 189;$1323 D) 252;$1764

14) Thepricep(indollars)andthequantityxsoldofacertainproductobeythedemandequation

p=–5x+140,0≤x≤28.

Whatpriceshouldthecompanychargetomaximizerevenue?

A) $14 B) $16.8 C) $21 D) $7

15) Theprofitthatthevendormakesperdaybysellingxpretzelsisgivenbythefunction

P(x)=–0.002x2+1.4x–400.Findthenumberofpretzelsthatmustbesoldtomaximizeprofit.

A) 350pretzels B) 700pretzels C) 0.7 pretzels D) –155 pretzels

16) TheownerofavideostorehasdeterminedthattheprofitsPofthestoreareapproximatelygivenby

P(x)=–x2+120x+76,wherexisthenumberofvideosrenteddaily.Findthemaximumprofittothe

nearestdollar.

A) $3676 B) $3600 C) $7276 D) $7200

17) Youhave296feetoffencingtoenclosearectangularregion.Findthedimensionsoftherectanglethat

maximizetheenclosedarea.

A) 74ftby74ft B) 148ftby148 ft C) 148 ftby37 ft D) 76ftby72 ft

18) Adeveloperwantstoenclosearectangulargrassylotthatbordersacitystreetforparking.Ifthe

developerhas352feetoffencinganddoesnotfencethesidealongthestreet,whatisthelargestareathat

canbeenclosed?

A) 15,488ft2B) 30,976ft2C) 7744ft2D) 23,232ft2

19) Youhave228feetoffencingtoenclosearectangularregion.Whatisthemaximumarea?

A) 3249squarefeet B) 12,996 squarefeet C) 51,984 squarefeet D) 3245 squarefeet

20) Youhave72feetoffencingtoenclosearectangularplotthatbordersonariver.Ifyoudonotfencethe

sidealongtheriver,findthelengthandwidthoftheplotthatwillmaximizethearea.

A) length:36feet,width:18feet B) length:54 feet,width:18feet

C) length:36feet,width:36feet D) length:18 feet,width:18feet

21) Aprojectileisfiredfromacliff600feetabovethewaterataninclinationof45°tothehorizontal,witha

muzzlevelocityof290feetpersecond.Theheighthoftheprojectileabovethewaterisgivenby

h(x)=–32x2

(290)2

+x+600,wherexisthehorizontaldistanceoftheprojectilefromthebaseofthecliff.Find

themaximumheightoftheprojectile.

A) 1257.03ft B) 1314.06 ft C) 657.03 ft D) 2571.09 ft

Page67

22) Aprojectileisfiredfromacliff600feetabovethewaterataninclinationof45°tothehorizontal,witha

muzzlevelocityof250feetpersecond.Theheighthoftheprojectileabovethewaterisgivenby

h(x)=–32x2

(250)2

+x+600,wherexisthehorizontaldistanceoftheprojectilefromthebaseofthecliff.How

farfromthebaseofthecliffistheheightoftheprojectileamaximum?

A) 976.56ft B) 1088.28 ft C) 488.28 ft D) 2064.84 ft

23) Considerthequadraticmodelh(t)=–16t2+40t+50fortheheight(infeet),h,ofanobjecttsecondsafter

theobjecthasbeenprojectedstraightupintotheair.Findthemaximumheightattainedbytheobject.

Howmuchtimedoesittaketofallbacktotheground?Assumethatittakesthesametimeforgoingup

andcomingdown.

A) maximumheight=75ft;timetoreachground=2.5seconds

B) maximumheight=75ft;timetoreachground=1.25seconds

C) maximumheight=50ft;timetoreachground=1.25seconds

D) maximumheight=50ft;timetoreachground=2.5seconds

24) Anobjectispropelledverticallyupwardfromthetopofa96–footbuilding.Thequadraticfunction

s(t)=–16t2+224t+96modelstheballʹsheightabovetheground,s(t),infeet,tsecondsafteritwasthrown.

Howmanysecondsdoesittakeuntiltheobjectfinallyhitstheground?Roundtothenearesttenthofa

secondifnecessary.

A) 14.4seconds B) 0.4seconds C) 7 seconds D) 2seconds

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

25) Asuspensionbridgehastwintowersthatare1300feetapart.Eachtowerextends180feetabovetheroad

surface.Thecablesareparabolicinshapeandaresuspendedfromthetopsofthetowers.Thecablestouch

theroadsurfaceatthecenterofthebridge.Findtheheightofthecableatapoint200feetfromthecenter

ofthebridge.

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

26) Alanisbuildingagardenshapedlikearectanglewithasemicircleattachedtooneshortside.Ifhehas70

feetoffencingtogoaroundit,whatdimensionswillgivehimthemaximumareainthegarden?

A) width=140

π+4

≈19.6,length=9.8 B) width=70

π+4

≈9.8,length=19.6

C) width=140

π+8

≈12.6,length=18.8 D) width=140

π+4

≈19.6,length=25.2

27) Thequadraticfunctionf(x)=0.0039x2–0.47x+36.01modelsthemedian,oraverage,age,y,atwhichU.S.

menwerefirstmarriedxyearsafter1900.Inwhichyearwasthisaverageageataminimum?(Roundto

thenearestyear.)Whatwastheaverageageatfirstmarriageforthatyear?(Roundtothenearesttenth.)

A) 1960

,

21.8yearsold B) 1960

,

50.2 yearsold

C) 1936,50.2yearsold D) 1953

,

36yearsold

Page68

4.4 BuildQuadraticModelsfromVerbalDescriptionsandfromData

1 BuildQuadraticModelsfromVerbalDescriptions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Aprojectileisthrownupwardsothatitsdistanceabovethegroundaftertsecondsish=–13t2+390t.

Afterhowmanysecondsdoesitreachitsmaximumheight?

A) 15sB)7s C) 22.5 sD)30s

2) Alanisbuildingagardenshapedlikearectanglewithasemicircleattachedtooneshortsidealongits

diameter.Thediameterofthesemicircleisequaltothewidthoftheshortsideoftherectangle.Ifhehas60

feetoffencingtogoaroundthegarden,whatdimensionswillgivehimthemaximumareainthegarden?

A) width=120

π+4

≈16.8,length=8.4 B) width=60

π+4

≈8.4,length=16.8

C) width=120

π+8

≈10.8,length=16.1 D) width=120

π+4

≈16.8,length=21.6

3) ThenumberofmosquitoesM(x),inmillions,inacertainareadependsontheJunerainfallx,ininches:

M(x)=4x–x2.Whatrainfallproducesthemaximumnumberofmosquitoes?

A) 2in. B) 0in. C) 16 in. D) 4in.

4) ThemanufacturerofaCDplayerhasfoundthattherevenueR(indollars)is

R(p)=–5p2+1980p,whentheunitpriceispdollars.Ifthemanufacturersetsthepriceptomaximize

revenue,whatisthemaximumrevenuetothenearestwholedollar?

A) $196,020 B) $392,040 C) $784,080 D) $1,568,160

5) Aprojectileisthrownupwardsothatitsdistanceabovethegroundaftertsecondsish=–11t2+264t.

Afterhowmanysecondsdoesitreachitsmaximumheight?

A) 12sB)6sC)18sD)24s

6) TheownerofavideostorehasdeterminedthatthecostC,indollars,ofoperatingthestoreis

approximatelygivenbyC(x)=2x2–28x+780,wherexisthenumberofvideosrenteddaily.Findthe

lowestcosttothenearestdollar.

A) $682 B) $388 C) $584 D) $878

7) Adeveloperwantstoenclosearectangulargrassylotthatbordersacitystreetforparking.Ifthe

developerhas260feetoffencinganddoesnotfencethesidealongthestreet,whatisthelargestareathat

canbeenclosed?

A) 8450ft2B) 16,900ft2C) 4225ft2D) 12,675ft2

8) Thequadraticfunctionf(x)=0.0039x2–0.48x+36.57modelsthemedian,oraverage,age,y,atwhichU.S.

menwerefirstmarriedxyearsafter1900.Inwhichyearwasthisaverageageataminimum?(Roundto

thenearestyear.)Whatwastheaverageageatfirstmarriageforthatyear?(Roundtothenearesttenth.)

A) 1962

,

21.8yearsold B) 1962

,

51.3 yearsold

C) 1936,51.3yearsold D) 1954

,

36yearsold

Page69

2 BuildQuadraticModelsfromData

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Useagraphingcalculatortoplotthedataandfindthequadraticfunctionofbestfit.

1) SouthernGraniteandMarblesellsgraniteandmarblebythesquareyard.Oneofitsgranitepatternsis

pricesensitive.Ifthepriceistoolow,customersperceivethatithaslessquality.Ifthepriceistoohigh,

customersperceivethatitisoverpriced.Thecompanyconductedapricingtestwithpotentialcustomers.

Thefollowingdatawascollected.Useagraphingcalculatortoplotthedata.Whatisthequadratic

functionofbestfit?

Price,xBuyers,B

$20 30

$30 50

$40 65

$60 75

$80 72

$100 50

$110 25

A) B(x)=–0.0243x2+3.115x–22.13 B) B(x)=0.0243x2–3.115x–22.13

C) B(x)=–0.243x2+3.115x–22.13 D) B(x)=–0.0243x2+3.115x+22.13

2) Arockisdroppedfromatallbuildinganditsdistance(infeet)belowthepointofreleaseisrecordedas

accuratelyaspossibleatvarioustimesafterthemomentofrelease.Theresultsareshowninthetable.

Findtheregressionequationofthebestmodel.

x(secondsafterrelease) 1 23456

y(distanceinfeet) 16 63 146 255 403 572

A) y=15.95x2B) y=–148.4+112x C) y= –74.9+290lnx D) y=13.0e0.686x

3) AnengineercollectsdatashowingthespeedsofagivencarmodelanditsaveragemilespergallonM.

Useagraphingcalculatortoplotthescatterdiagram.Whatisthequadraticfunctionofbestfit?

Speed,smph,M

20 18

30 20

40 23

50 25

60 28

70 24

80 22

A) M(s)=–0.0063x2+0.720x+5.142 B) M(s)=–0.631x2+0.720x+5.142

C) M(s)=0.063x2+0.720x+5.142 D) M(s)=–6.309x2+0.720x+5.142

Page70

4) Thenumberofhousingstartsinonebeachsidecommunityremainedfairlyleveluntil1992andthenbegan

toincrease.Thefollowingdatashowsthenumberofhousingstartssince1992(x=1).Useagraphing

calculatortoplotascatterdiagram.Whatisthequadraticfunctionofbestfit?

Year,xHousingStarts,H

1200

2205

3210

4240

5245

6230

7220

8210

A) H(x)=–2.679x2+26.607x+168.571 B) H(x)=2.679x2+26.607x+168.571

C) H(x)=–2.679x2–26.607x+168.571 D) H(x)=–2.679x2+26.607x–168.571

5) Thenumberofhousingstartsinonebeachsidecommunityremainedfairlyleveluntil1992andthenbegan

toincrease.Thefollowingdatashowsthenumberofhousingstartssince1992(x=1).Useagraphing

calculatortoplotascatterdiagram.Whatisthequadraticfunctionofbestfit?

Year,xHousingStarts,H

1200

2210

3230

4240

5250

6230

7215

8208

A) H(x)=–3.268x2+30.494x+168.982 B) H(x)=3.268x2+30.494x+168.982

C) H(x)=–3.268x2–30.494x+168.982 D) H(x)=–3.268x2+30.494x–168.982

6) Asmallmanufacturingfirmcollectedthefollowingdataonadvertisingexpenditures(inthousandso

f

dollars)andtotalrevenue(inthousandsofdollars).

Advertising,xTotalRevenue,R

25

28

31

32

34

39

40

45

6430

6432

6434

6431

6432

6420

Findthequadraticfunctionofbestfit.

A) R(x)=–0.091x2+5.95x+6337 B) R(x)=–0.024x2+7.13x+6209

C) R(x)=–0.31x2+2.63x+6128 D) R(x)=–0.015x2+4.53x+6123

Page71

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

7) Thefollowingdatarepresentsthetotalrevenue,R(indollars),receivedfromsellingxbicyclesatTunneyʹs

BicycleShop.Usingagraphingutility,findthequadraticfunctionofbestfitusingcoefficientsroundedto

thenearesthundredth.

NumberofBicycles,xTotalRevenue,R(indollars)

0

22

70

96

149

200

230

250

0

27,000

46,000

55,200

61,300

64,000

64,500

67,000

8) ThefollowingtableshowsthemediannumberofhoursofleisuretimethatAmericanshadeachweekin

variousyears.

Year 1973 1980 1987 1993 1997

Median#ofLeisurehrsperWeek 26.2 19.2 16.6 18.8 19.5

Usex=0torepresenttheyear1973.Usingagraphingutility,determinethequadraticregressionequation

forthedatagiven.WhatyearcorrespondstothetimewhenAmericanshadtheleasttimetospendon

leisure?

4.5 InequalitiesInvolvingQuadraticFunctions

1 SolveInequalitiesInvolvingaQuadraticFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usethefiguretosolvetheinequality.

1) f(x)

<

0

x

-16 -12 -8 -4 4 8 12 16

y

16

12

8

4

-4

-8

-12

-16

(-2, 0) (3, 0)

x

-16 -12 -8 -4 4 8 12 16

y

16

12

8

4

-4

-8

-12

-16

(-2, 0) (3, 0)

A) {x|–2

<

x

<

3};(–2

,

3) B) {x|–2≤x≤3};[–2

,

3]

C) {x|x≤–2orx≥3};(–∞

,

–2]or[3

,

∞) D) {x|x

<

–2 orx>3};(–∞

,

–2)or(3

,

∞)

Page72

2) g(x)≤0

x

–16 -12 –8 –4 4 8 12 16

y

16

12

8

4

-4

-8

-12

-16

(-4, 0) (4, 0)

x

–16 -12 –8 –4 4 8 12 16

y

16

12

8

4

-4

-8

-12

-16

(-4, 0) (4, 0)

A) {x|x≤–4orx≥4};(–∞

,

–4]or[4

,

∞) B) {x|–4≤x≤4};[–4

,

4]

C) {x|–4

<

x

<

4};(–4

,

4) D) {x|x

<

–4 orx>4};(–∞

,

–4)or(4

,

∞)

3)

g(x)≥f(x)

A) {x|–1≤x≤2};[–1,2] B) {x|–1

<

x

<

2};(–1,2)

C) {x|x

<

–1orx>2};(–∞

,

–1)or(2,∞) D) {x|x≤–1orx≥2};(–∞

,

–1]or[2,∞)

Page73

4)

f(x)>g(x)

A) {x|x

<

–1orx>2};(–∞

,

–1)or(2,∞) B) {x|x≤–1orx≥2};(–∞

,

–1]or[2,∞)

C) {x|–1≤x≤2};[–1,2] D) {x|–1

<

x

<

2};(–1,2)

5)

f(x)<g(x)

A) {x|x

<

–1orx>3};(–∞

,

–1)or(3,∞) B) {x|–1≤x≤3};[–1,3]

C) {x|–1

<

x

<

3};(–1,3) D) {x|x≤–1orx≥3};(–∞

,

–1]or[3,∞)

Page74

6)

f(x)≥g(x)

A) {x|–1≤x≤3};[–1,3] B) {x|–1

<

x

<

3};(–1,3)

C) {x|x

<

–1orx>3};(–∞

,

–1)or(3,∞) D) {x|x≤–1orx≥3};(–∞

,

–1]or[3,∞)

Solvetheinequality.

7) x2–2x–3≤0

A) [–1

,

3] B) (–∞

,

–1] C) [3

,

∞)D)(

–∞

,

–1]or[3

,

∞)

8) x2+2x–24>0

A) (–∞

,

–6)or(4

,

∞)B)(

–6

,

4) C) (–∞

,

–6) D) (4

,

∞)

9) x2–5x≥0

A) (–∞

,

0]or[5

,

∞) B) [0,5] C) (–∞

,

–5]or[0,∞)D)[

–5

,

0]

10) x2+5x≥0

A) (–∞

,

–5]or[0,∞) B) [0,5] C) (–∞

,

0]or[5

,

∞)D)[

–5

,

0]

11) x2+2x≤0

A) [–2

,

0] B) [0,2] C) (–∞

,

–2]or[0,∞)D)(

–∞

,

0]or[2

,

∞)

12) x2–2x≤0

A) [0,2] B) [–2

,

0] C) (–∞

,

–2]or[0,∞)D)(

–∞

,

0]or[2

,

∞)

13) x2–9>0

A) (–∞

,

–3)or(3

,

∞)B)(

–3

,

3) C) (–∞

,

–9)or(9

,

∞)D)(

–9

,

9)

14) x2–16≤0

A) [–4

,

4] B) (–∞

,

–4]or[4

,

∞)

C) (–∞

,

–16]or[16

,

∞)D)[

–16

,

16]

15) x2+2x≥8

A) (–∞

,

–4]or[2

,

∞)B)[

–4

,

2] C) (–∞

,

–4] D) [2

,

∞)

16) 2x2–4<–7x

A) –4,1

2B) 1

2,4 C) –4,–1

2D) –1

2,4

Page75

17) 36x2+49<84x

A) Norealsolution B) –∞,7

6C) –∞,–7

6D) –7

6,∞

18) 70(x2–1)>51x

A) –∞,–7

10

or10

7,∞B) –7

10,10

7

C) –∞,–10

7

or7

10,∞D) –10

7,7

10

Solvetheproblem.

19) Iff(x)=6x2–5xandg(x)=2x+3,solveforf(x)=g(x)

A) –1

2,1 B) 3

2,–1

3C) 1

6,1 D) 1

3,–3

2

20) Iff(x)=6x2–5xandg(x)=2x+3,solvef(x)≤g(x).

A) –1

3, 3

2B) –3

2,1

3C) –1

3,3

2D) –1

3, 3

2

21) Ifg(x)=56x2–56andh(x)=15x,thensolveg(x)>h(x).

A) –∞,–7

8

or8

7,∞B) –8

7,7

8C) –7

8,8

7D) –∞,–8

7

or7

8,∞

22) Ifh(x)=x2–6x+5,solveh(x)>0.

A) (–∞

,

1)or(5

,

∞)B)(1

,

5) C) (–∞

,

1) D) (5

,

∞)

23) Ifg(x)=x2–2x–8,solveg(x)≤0.

A) [–2

,

4] B) (–∞

,

–2] C) [4

,

∞)D)(

–∞

,

–2]or[4

,

∞)

24) Therevenueachievedbysellingxgraphingcalculatorsisfiguredtobex(38 –0.2x)dollars.Thecostof

eachcalculatoris$22.Howmanygraphingcalculatorsmustbesoldtomakeaprofit(revenue–cost)ofat

least$303.80?

A) {x∣31

<

x

<

49} B) {x∣11

<

x

<

29} C) {x∣32

<

x

<

30} D) {x∣33

<

x

<

47}

25) Arockfallsfromatowerthatis336fthigh.Asitisfalling,itsheightisgivenbytheformulah=336–16t2.

Howmanysecondswillittakefortherocktohittheground(h=0)?

A) 4.6s B) 18.3 s C) 7056 s D) 17.9 s

26) Arockfallsfromatowerthatis68.6mhigh.Asitisfalling,itsheightisgivenbytheformula

h=68.6–4.9t2.Howmanysecondswillittakefortherocktohittheground(h=0)?

A) 3.7s B) 8.3s C) 1000 sD)8s

27) Aflarefiredfromthebottomofagorgeisvisibleonlywhentheflareisabovetherim.Ifitisfiredwithan

initialvelocityof96ft/sec,andthegorgeis128ftdeep,duringwhatintervalcantheflarebeseen?(h=

–16t2+vot+ho.)

A) 2

<

t

<

4B)4

<

t

<

6C)0

<

t

<

2D)6

<

t

<

8

Page76

28) Acoinistossedupwardfromabalcony146 fthighwithaninitialvelocityof16ft/sec.Duringwhat

intervaloftimewillthecoinbeataheightofatleast50ft?(h=–16t2+vot+ho.)

A) 0≤t≤3B)0≤t≤1C)3

≤t≤6D)2≤t≤3

29) Ifarocketispropelledupwardfromgroundlevel,itsheightinmetersaftertsecondsisgivenby

h=–9.8t2+127.4t.Duringwhatintervaloftimewilltherocketbehigherthan411.6m?

A) 6

<

t

<

7B)0

<

t

<

6C)7

<

t

<

12 D) 12

<

t

<

13

30) Aflarefiredfromthebottomofagorgeisvisibleonlywhentheflareisabovetherim.Ifitisfiredwithan

initialvelocityof112ft/sec,andthegorgeis192ftdeep,duringwhatintervalcantheflarebeseen?

(h=–16t2+vot+ho.)

A) 3

<

t

<

4B)6

<

t

<

7C)0

<

t

<

3D)9

<

t

<

10

31) Acoinistossedupwardfromabalcony188 ft highwithaninitialvelocityof32ft/sec.Duringwhat

intervaloftimewillthecoinbeataheightofatleast60ft?

(h=–16t2+vot+ho.)

A) 0≤t≤4B)0≤t≤1C)4

≤t≤8D)3≤t≤4

32) Ifarocketispropelledupwardfromgroundlevel,itsheightinmetersaftertsecondsisgivenby

h=–9.8t2+88.2t.Duringwhatintervaloftimewilltherocketbehigherthan137.2m?

A) 2

<

t

<

7B)0

<

t

<

2C)7

<

t

<

4D)4

<

t

<

9

Page77

Ch.4 LinearandQuadraticFunctions

AnswerKey

4.1 PropertiesofLinearFunctionsandLinearModels

1 GraphLinearFunctions

2 UseAverageRateofChangetoIdentifyLinearFunctions

3 DetermineWhetheraLinearFunctionIsIncreasing,Decreasing,orConstant

4 BuildLinearModelsfromVerbalDescriptions

4.2 BuildingLinearModelsfromData

1 DrawandInterpretScatterDiagrams

Page79

2 DistinguishbetweenLinearandNonlinearRelations

3 UseaGraphingUtilitytoFindtheLineofBestFit

Page80

4.3 QuadraticFunctionsandTheirProperties

1 GraphaQuadraticFunctionUsingTransformations

Page81

2 IdentifytheVertexandAxisofSymmetryofaQuadraticFunction

3 GraphaQuadraticFunctionUsingItsVertex,Axis,andIntercepts

4 FindaQuadraticFunctionGivenItsVertexandOneOtherPoint

5 FindtheMaximumorMinimumValueofaQuadraticFunction

Page82

4.4 BuildQuadraticModelsfromVerbalDescriptionsandfromData

1 BuildQuadraticModelsfromVerbalDescriptions

2 BuildQuadraticModelsfromData

4.5 InequalitiesInvolvingQuadraticFunctions

1 SolveInequalitiesInvolvingaQuadraticFunction

Page83

Page84