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) = 10x + 5
A) m = 10; b = 5B)m =10; b = –5C)m
= –10; b =5D)m
= –10; b = –5
2) h(x) = –12x – 10
A) m = –12; b = – 10 B) m =12; b =10 C) m =12; b = – 10 D) m = –12; b =10
3) p(x) = –x + 8
A) m = –1; b =8B)m
=1; b = – 8C)m
= –1; b = – 8D)m
=0; b =8
4) f(x) = 9
5x + 1
A) m = 9
5; b = 1B)m = 1; b = 9
5C) m = 5
9; b = – 1D)m = – 9
5; b = – 1
5) F(x) = 1
A) m = 0; b = 1B)m =1; b =0C)m
=0; b =0D)m
=1; b =1
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
3x
A) m = 1
3; b = 0B)m =3; b =0C)m
= – 1
3; b = 0D)m = 0; b = 1
3
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 – 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 4
11) f(x) = 2
5x – 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 5
12) h(x) = – 3
4x – 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 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
5x
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)
318
530
742
954
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) = 7x + 1
A) 7 B) –1C)1 D)
–7
2) h(x) = –5x – 6
A) –5B)5 C)
–6D)6
3) p(x) = –x – 7
A) –1 B) 1 C) 7 D) –7
4) F(x) = 10
A) 0 B) 1
10 C) –10 D) 10
5) f(x) = 3
4x + 1
A) 3
4B) – 3
4C) 1 D) – 1
6) h(x) = – 2
5x + 2
A) – 2
5B) 2
5C) 2 D) – 2
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) = 3x + 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) 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) = 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) 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) = –4x + 5
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) = –2x – 6
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 + 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) 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) = 1
2x + 3
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) = – 1
2x – 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) = –8
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 – 2 and g(x) = x –11.
(a) Solve f(x) = 0.
(b) Solve g(x) = 0.
(c) Solve f(x) = g(x).
A) (a) x = –2; (b) x = 11; (c) x = 4.5 B) (a) x = –2; (b) x = 11; (c) x = –6.5
C) (a) x = 2; (b) x = 11; (c) x = 4.5 D) (a) x = –2; (b) x = –11; (c) x = 4.5
Page 18
2) Suppose that f(x) = –x – 8 and g(x) = x –18.
(a) Solve f(x) > 0.
(b) Solve g(x) > 0.
(c) Solve f(x) ≤ g(x).
A) (a) x
–8; (b) x > 18; (c) x ≥ 5 B) (a) x
–8; (b) x
18; (c) x ≥ –13
C) (a) x > 8; (b) x > 18; (c) x > 5 D) (a) x
–8; (b) x
–18; (c) x ≤ 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 = 1B)x = 4C)x = –1D)x
= –4
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 ≤ 1B)x ≥ 1C)x ≥–2D)x
–2
6) A truck rental company rents a moving truck one day by charging $25 plus $0.07 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 160 miles?
A) C(x) = 0.07x + 25; $36.20 B) C(x) =25x +0.07; $4000.07
C) C(x) = 0.07x + 25; $26.12 D) C(x) =0.07x –25; –$13.80
7) Linda needs to have her car towed. Little Town Auto charges a flat fee of $55 plus $2 per mile towed.
Write a function expressing Linda’s towing cost, c, in terms of miles towed, x. Find the cost of having a car
towed 2 miles.
A) c(x) = 2x + 55; $59 B) c(x) =2x; $4 C) c(x) =2x +55; $49 D) c(x) =2x; $57
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(1.5), the velocity of the object at time t = 1.5 seconds.
A) V(1.5) = 58 feet per second B) V(1.5) =59.3 feet per second
C) V(1.5) = 57.3 feet per second D) V(1.5) =56 feet per second
11) The cost for labor associated with fixing a washing machine is computed as follows: There is a fixed charge
of $25 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) = 25 + 29x B) C(x) =29 +25x C) C(x) =( 25 +29) x D) C(x) =25 –29x
Page 20
12) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.80 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.
A) C(x) = 2.80 + 1.95x B) C(x) =1.95 +2.80x C) C(x) =4.75x D) C(x) =3.25x
13) In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $2.55 as soon as
you get in the taxi, to which a charge of $2.35 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 8–mile taxi ride.
A) $21.35 B) $21.53 C) $21.23 D) $22.25
14) Marty’s 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 $610 to set up for production, and variable costs of $30
per jacket. Write an equation that can be used to determine the total cost, C(x), encountered by Marty’s
Company in producing x jackets.
A) C(x) = 610 + 30x B) C(x) =610x +30 C) C(x) =(610 +30) x D) C(x) =610 –30x
15) Marty’s 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 $660 to set up for production, and variable costs of $42
per jacket. Write an equation that can be used to determine the total cost, C(x), encountered by Marty’s
Company in producing x jackets, and use the equation to find the total cost of producing 75 jackets.
A) $3810 B) $3822 C) $3790 D) $3802
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) = 4750 – 70p and D(p) = 120p, where p is the price. Find the equilibrium
price for caps at the game. Then find the equilibrium quantity.
A) $25
,
$3000 B) $50
,
$1250 C) $39
,
$2020 D) $50
,
$3000
17) Regrind, Inc. regrinds used typewriter platens. The variable cost per platen is $1.60. The total cost to
regrind 100 platens is $400. Find the linear cost function to regrind platens. If reground platens sell for $
10.10 each, how many must be reground and sold to break even?
A) C(x) = 1.60x + 240; 29 platens B) C(x) =1.60x +400; 47 platens
C) C(x) = 1.60x + 400; 35 platens D) C(x) =1.60x +240; 21 platens
18) Northwest Molded molds plastic handles which cost $0.10 per handle to mold. The fixed cost to run the
molding machine is $3786 per week. If the company sells the handles for $2.10 each, how many handles
must be molded and sold weekly to break even?
A) 1893 handles B) 1262 handles C) 37,860 handles D) 1720 handles
19) A lumber yard has fixed costs of $6087.70 per day and variable costs of $0.6 per board–foot produced.
Lumber sells for $2.30 per board–foot. How many board–feet must be produced and sold daily to break
even?
A) 3581 board–feet B) 2387 board–feet C) 10,146 board–feet D) 2099 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 –9 22 –7 1 19 1 17 –4–4
y 56 20 42 –17 1 32 7 64 –6 3
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 18 19 30 50 60 67 80 79 88
y132136497052729178
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 (2
,
1.0) and
(9, 4.4). Graph the line on the scatter diagram.
x 2 3 5 8 9
y 1.0 2.1 2.8 3.4 4.4
Page 23
x
246810
y
5
4
3
2
1
x
246810
y
5
4
3
2
1
A) y = 0.49x + 0.03
x
246810
y
5
4
3
2
1
x
246810
y
5
4
3
2
1
B) y =0.4x +0.2
x
246810
y
5
4
3
2
1
x
246810
y
5
4
3
2
1
C) y = 0.53x + 0.03
x
246810
y
5
4
3
2
1
x
246810
y
5
4
3
2
1
D) y =0.48x +0.1
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, 3.1). Graph the line on the scatter diagram.
x 1.2 2.0 2.9 3.7 4.6
y 9.5 8.3 5.7 4.6 3.1
Page 24
x
12345
y
14
12
10
8
6
4
2
x
12345
y
14
12
10
8
6
4
2
A) y = –2x + 12.3
x
12345
y
14
12
10
8
6
4
2
x
12345
y
14
12
10
8
6
4
2
B) y = –1.53x +10.14
x
12345
y
14
12
10
8
6
4
2
x
12345
y
14
12
10
8
6
4
2
C) y = 2x + 12.3
x
12345
y
14
12
10
8
6
4
2
x
12345
y
14
12
10
8
6
4
2
D) y = –2.2x +12.8
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 12 18 24 30 36
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
61 110
68 157
74 196
66 171
62 127
70 180
67 184
Graph the data on a scatter diagram treating height as the independent variable. Find an equation of the
line containing the points (62, 127) 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 70.3 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 earth’s 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 7.2
33.7 6.9
34.4 6.3
36.5 5.3
38.1 4.9
39.9 4.4
41.6 4.0
43.2 3.3
44.0 3.1
Graph the data on a scatter diagram treating latitude as the independent variable. Find an equation of the
line containing the points (32.4, 7.2) 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 34.1 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 + 2.57 B) y = 0.30x +4.29 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 = 1.91x + 5.05 B) y = 2.03x +2.36 C) y =1.53x +10.7 D) y = –0.33x +75.3
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 = 1.02x + 11.7 B) y = 1.35x +2.81 C) y =2.02x –47.3 D) y = –0.67x +92.3
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 130 pounds?
Body
Weight (lbs)
Drug
Dosage (mg)
50 10
100 13
150 15
200 19
250 21
A) 14.48 mg B) 22.86 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 feet 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) 9.6 ft B) 15.7 ft C) 10.5 ft D) 10.3 ft
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
hundredth)?
CD Maturity (yrs) Interest rate (%)
5 8.458
10 8.470
15 8.496
20 8.580
25 8.625
A) 8.66% B) 8.68% C) 9.06% D) 8.87%
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 rock’s horizontal distance, d (in feet) from Sally and the initial speed
with which she throws.
Initial speed( in ft/sec), v 10 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 feet per second.
A) 31.34 ft B) 26.67 ft C) 34.76 ft D) 31.33 ft
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 Women’s 100 m Freestyle.
year 1988 1992 1996 2000 2004 2008 2012
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 2016.
24) The following data represents the Olympic winning time in Women’s 100 m Freestyle.
year 1988 1992 1996 2000 2004 2008 2012
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 + 1 B) f(x) = x2 – 2x + 1 C) f(x) = x2 + 2x D) f(x) = x2 – 2x
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 + 6x B) f(x) = x2 + 6x C) f(x) = –x2 + 6 D) f(x) = x2 + 6
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 + 12 B) f(x) = x2 + 12x C) f(x) = –x2 + 12x D) f(x) = –x2 + 12
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– 3
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) = 4x2
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
5x2
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
3x2 + 2
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) = –4x2 – 2
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) = 5x2 – 6
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 – 2x
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 + 2x – 8
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) = 5x2 – 10x + 8
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) = 2
7x2 + 4
7x – 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 + 4x – 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
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 + 4x
A) (–2
,
–4); x = –2B)(
–4
,
2); x = –4C)(2
,
–4); x =2D)(4
,
–2); x =4
2) f(x) = x2 – 4x
A) (2
,
–4); x = 2B)(
–4
,
2); x = –4C)(
–2
,
4); x = –2D)(4
,
–2); x =4
Page 52
3) f(x) = –x2 + 6x
A) (3
,
9); x = 3B)(
–9
,
3); x = –9C)(
–3
,
–9); x = –3D)(9
,
–3); x =9
4) f(x) = –x2 – 10x
A) (–5
,
25); x = –5B)(
–25
,
5); x = –25 C) (5
,
–25); x =5D)(25
,
–5); x =25
5) f(x) = –3x2 – 24x
A) (–4
,
48); x = –4B)(4
,
48); x =4C)(
–4
,
0); x = –4D)(4
,
0); x =4
6) f(x) = x2 + 6x + 8
A) (–3
,
–1); x = –3B)(3
,
–1); x =3C)(3
,
1); x =3D)(
–3
,
1); x = –3
7) f(x) = –x2 – 10x – 6
A) (–5
,
19) ; x = –5B)(5
,
–81) ; x =5C)(
–10
,
–6) ; x = –10 D) (5
,
–31) ; x =5
8) f(x) = 4x2 – 8x + 7
A) (1
,
3) ; x = 1B)(
–1
,
19) ; x = –1C)(2
,
15) ; x =2D)(
–2
,
39) ; x = –2
9) f(x) = x2 + 3x – 2
A) – 3
2, – 17
4 ; x = – 3
2B) 3
2, 19
4 ; x = 3
2
C) (–1
,
–2) ; x = –1D)(3
,
16) ; x =3
10) f(x) = –12x2 – 2x – 3
A) – 1
12, – 35
12 ; x = – 1
12 B) (12
,
–3); x =12
C) 1
12, 35
12 ; x = 1
12 D) –12, – 35
12 ; x = –12
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 – 6x
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
A) vertex (3
,
–9)
intercepts (0, 0), (6, 0)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
B) vertex (–3
,
–9)
intercepts (0, 0), (–6, 0)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
C) vertex (–3
,
9)
intercept (0, 18)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
D) vertex (3
,
9)
intercept (0, 18)
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 + 10x
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
A) vertex (5
,
25)
intercepts (0, 0), (10, 0)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
B) vertex (5
,
–25)
intercept (0, –50)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
C) vertex (–5
,
25)
intercepts (0, 0), (– 10, 0)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
D) vertex (–5
,
–25)
intercept (0, –50)
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 – 12x + 36
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
A) vertex (6
,
0)
intercepts (0, 36), (6, 0)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
B) vertex (–6
,
0)
intercepts (0, 36), (–6, 0)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
C) vertex (–6
,
36)
intercept (0, 72)
x
-10 -5 5 10
y
40
20
-20
-40
x
-10 -5 5 10
y
40
20
-20
-40
D) vertex (6
,
36)
intercept (0, 72)
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 + 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 (–1, 0), (– 7, 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 (1, 0), (7, 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 (1, 0), (7, 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 (–1, 0), (– 7, 0), (0, –7)
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 – 8
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) vertex (–3
,
1)
intercepts (–2, 0), (– 4, 0), (0, –8)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) vertex (3
,
–1)
intercepts (2, 0), (4, 0), (0, 8)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) vertex (3
,
1)
intercepts (2, 0), (4, 0), (0, –8)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) vertex (–3
,
–1)
intercepts (–2, 0), (– 4, 0), (0, 8)
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 – 4x – 5
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) vertex (2
,
–9)
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 (–2
,
–9)
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 (–2
,
9)
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 (2
,
9)
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 59
7) f(x) = –x2 + 6x – 8
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) vertex (3
,
1)
intercepts (4, 0), (2, 0), (0, –8)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) vertex (–3
,
–1)
intercepts (–4, 0), (– 2, 0), (0, 8)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) vertex (–3
,
1)
intercepts (–4, 0), (– 2, 0), (0, –8)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) vertex (3
,
–1)
intercepts (4, 0), (2, 0), (0, 8)
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) = –2x2 – 8x – 13
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
A) vertex (–2
,
–5)
intercept (0, –13)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
B) vertex (2
,
–5)
intercept (0, –13)
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
C) vertex (–2
,
–5)
intercept 0,
– 7
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
D) vertex (2
,
–5)
intercept 0,
– 7
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) = –10x2 – 2x – 3
x
–10–8-6-4-2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x
–10–8-6-4-2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
A) vertex – 1
10, – 29
10
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
10, 29
10
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
10, – 29
10
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
10, 29
10
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 + 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}
11) f(x) = –x2 – 4x
A) domain: all real numbers
range: {y|y ≤ 4}
B) domain: {x|x ≤–2}
range: {y|y ≤ 4}
C) domain: {x|x≤ 2}
range: {y|y ≤ 4}
D) domain: all real numbers
range: {y|y ≤ –4}
12) f(x) = x2 + 10x + 25
A) domain: all real numbers
range: {y|y ≥ 0}
B) domain: {x|x ≥–5}
range: {y|y ≥ 0}
C) domain: {x|x ≥ 5}
range: {y|y ≥ 0}
D) domain: all real numbers
range: {y|y ≥ 25}
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 – 6x – 8
A) domain: all real numbers
range: {y|y ≤ 1}
B) domain: {x|x ≤–3}
range: {y|y ≤ 1}
C) domain: {x|x ≤ –3}
range: {y|y ≤ –1}
D) domain: all real numbers
range: {y|y ≤ –1}
15) f(x) = x2 – 6x + 5
A) domain: all real numbers
range: {y|y ≥ –4}
B) domain: {x|x ≥–3}
range: {y|y ≥ –4}
C) domain: all real numbers
range: {y|y ≤ 4}
D) domain: all real numbers
range: all real numbers
16) f(x) = –x2 + 2x + 3
A) domain: all real numbers
range: {y|y ≤ 4}
B) domain: {x|x ≤–1}
range: {y|y ≤ 4}
C) domain: all real numbers
range: {y|y ≤ –4}
D) domain: all real numbers
range: all real numbers
17) f(x) = –6x2 – 2x – 10
A) domain: all real numbers
range: y y
≤– 59
6
B) domain: all real numbers
range: y y
≥– 59
6
C) domain: all real numbers
range: y y
≥59
6
D) domain: all real numbers
range: y y
≤59
6
Page 63
Determine where the function is increasing and where it is decreasing.
18) 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)
19) f(x) = –x2 + 4x
A) increasing on (–∞
,
2)
decreasing on (2, ∞)
B) increasing on (2
,
∞)
decreasing on (–∞, 2)
C) increasing on (–2
,
∞)
decreasing on (–∞, –2)
D) increasing on (–∞
,
–2)
decreasing on (–2, ∞)
20) f(x) = x2 – 12x + 36
A) increasing on (6
,
∞)
decreasing on (–∞, 6)
B) increasing on (–∞
,
6)
decreasing on (6, ∞)
C) increasing on (–∞
,
–6)
decreasing on (–6, ∞)
D) increasing on (–6
,
∞)
decreasing on (–∞, –6)
21) 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, ∞)
22) f(x) = –x2 – 6x – 8
A) increasing on (–∞
,
–3)
decreasing on (–3, ∞)
B) increasing on (–3
,
∞)
decreasing on (–∞, –3)
C) increasing on (–∞
,
1)
decreasing on (1, ∞)
D) increasing on (1
,
∞)
decreasing on (–∞, 1)
23) f(x) = x2 – 6x + 8
A) increasing on (3
,
∞)
decreasing on (–∞, 3)
B) increasing on (–∞
,
3)
decreasing on (3, ∞)
C) increasing on (–∞
,
–1)
decreasing on (–1, ∞)
D) increasing on (–1
,
∞)
decreasing on (–∞, –1)
24) f(x) = –x2 + 2x + 8
A) increasing on (–∞
,
1)
decreasing on (1, ∞)
B) increasing on (1
,
∞)
decreasing on (–∞, 1)
C) increasing on (9
,
∞)
decreasing on (–∞, 9)
D) increasing on (–∞
,
9)
decreasing on (9, ∞)
25) g(x) = 2x2 + 32x + 124
A) decreasing on (–∞
,
–8)
increasing on (–8, ∞)
B) increasing on (–∞
,
–16)
decreasing on (–16, ∞)
C) decreasing on (–∞
,
8)
increasing on (8, ∞)
D) increasing on (–∞
,
–8)
decreasing on (–8, ∞)
Page 64
26) f(x) = –3x2 – 2x – 4
A) increasing on –∞, – 1
3
decreasing on – 1
3, ∞
B) decreasing on –∞, – 1
3
increasing on – 1
3, ∞
C) increasing on –∞, 1
3
decreasing on 1
3, ∞
D) increasing on –∞, – 11
3
decreasing on – 11
3, ∞
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, –1)
(0, 3)
x
-5 5
y
5
-5
(-2, –1)
(0, 3)
A) f(x) =x2 + 4x + 3 B) f(x) = –x2 – 4x – 3 C) f(x) =x2 – 8x + 3 D) f(x) = –x2 + 4x + 3
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 + 9
A) minimum; 9 B) minimum; 0 C) maximum; 0 D) maximum; 9
2) f(x) = x2 – 2
A) minimum; –2 B) minimum; 0 C) maximum; –2 D) maximum; 0
3) f(x) = x2 + 2x – 7
A) minimum; – 8 B) maximum; –8 C) minimum; –1 D) maximum; –1
4) f(x) = –x2 – 2x – 8
A) maximum; – 7 B) minimum; –7 C) minimum; –1 D) maximum; –1
5) f(x) = 3x2 – 2x – 1
A) minimum; – 4
3B) maximum; – 4
3C) minimum; 1
3D) maximum; 1
3
6) f(x) = 4x2 – 4x
A) minimum; – 1 B) maximum; –1 C) minimum; 1
2D) maximum; 1
2
7) f(x) = –4x2 + 12x
A) maximum; 9 B) minimum; 9 C) minimum; –9 D) maximum; –9
8) f(x) = –7x2 – 2x – 8
A) maximum; – 55
7B) minimum; – 55
7C) maximum; 55
7D) minimum; 55
7
Solve the problem.
9) The manufacturer of a CD player has found that the revenue R (in dollars) is
R(p) = –4p2 + 1000p, 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) $62,500 B) $125,000 C) $250,000 D) $500,000
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 – 24x + 800, where x is the number of videos rented daily. Find the
lowest cost to the nearest dollar.
A) $728 B) $512 C) $656 D) $872
11) The price p and the quantity x sold of a certain product obey the demand equation
p = – 1
2x + 160, 0 ≤ x ≤ 320.
What quantity x maximizes revenue? What is the maximum revenue?
A) 160; $12,800 B) 80; $9600 C) 240; $9600 D) 320; $12,800
Page 66
12) The price p and the quantity x sold of a certain product obey the demand equation
p = – 1
5x + 200, 0 ≤ x ≤ 1000.
What price should the company charge to maximize revenue?
A) $100 B) $120 C) $150 D) $50
13) The price p (in dollars) and the quantity x sold of a certain product obey the demand equation
x = –9p + 180, 0 ≤ p ≤ 20.
What quantity x maximizes revenue? What is the maximum revenue?
A) 90; $900 B) 45; $675 C) 135; $675 D) 180; $900
14) The price p (in dollars) and the quantity x sold of a certain product obey the demand equation
p = –20x + 560, 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) = –0.004x2 + 2.4x – 100. Find the number of pretzels that must be sold to maximize profit.
A) 300 pretzels B) 600 pretzels C) 1.2 pretzels D) 260 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 + 68, where x is the number of videos rented daily. Find the maximum profit to the
nearest dollar.
A) $3668 B) $3600 C) $7268 D) $7200
17) You have 92 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that
maximize the enclosed area.
A) 23 ft by 23 ft B) 46 ft by 46 ft C) 46 ft by 11.5 ft D) 25 ft by 21 ft
18) A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the
developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that
can be enclosed?
A) 12,800 ft2B) 25,600 ft2C) 6400 ft2D) 19,200 ft2
19) You have 348 feet of fencing to enclose a rectangular region. What is the maximum area?
A) 7569 square feet B) 30,276 square feet
C) 121,104 square feet D) 7565 square feet
20) You have 96 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: 48 feet, width: 24 feet B) length: 72 feet, width: 24 feet
C) length: 48 feet, width: 48 feet D) length: 24 feet, width: 24 feet
21) A projectile is fired from a cliff 500 feet above the water at an inclination of 45° to the horizontal, with a
muzzle velocity of 350 feet per second. The height h of the projectile above the water is given by
h(x) = –32x2
(350)2 + x + 500, where x is the horizontal distance of the projectile from the base of the cliff. Find
the maximum height of the projectile.
A) 1457.03 ft B) 1914.06 ft C) 957.03 ft D) 3371.09 ft
Page 67
22) A projectile is fired from a cliff 100 feet above the water at an inclination of 45° to the horizontal, with a
muzzle velocity of 380 feet per second. The height h of the projectile above the water is given by
h(x) = –32x2
(380)2 + x + 100, 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) 2256.25 ft B) 1228.13 ft C) 1128.13 ft D) 3484.38 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 240–foot building. The quadratic function
s(t) = –16t2 + 144t + 240 models the ball’s 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) 10.4 seconds B) 1.4 seconds C) 4.5 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 50
feet of fencing to go around it, what dimensions will give him the maximum area in the garden?
A) width = 100
π + 4 ≈ 14, length = 7 B) width = 50
π + 4 ≈ 7, length = 14
C) width = 100
π + 8 ≈ 9, length = 13.5 D) width = 100
π + 4 ≈ 14, length = 18
27) The quadratic function f(x) = 0.0042x2 – 0.44x + 36.46 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) 1952
,
24.9 years old B) 1952
,
48 years old
C) 1936, 48 years old D) 1952
,
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 = –15t2 + 540t.
After how many seconds does it reach its maximum height?
A) 18 sec B) 9 sec C) 27 sec D) 36 sec
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 50
feet of fencing to go around the garden, what dimensions will give him the maximum area in the garden?
A) width = 100
π + 4 ≈ 14, length = 7 B) width = 50
π + 4 ≈ 7, length = 14
C) width = 100
π + 8 ≈ 9, length = 13.5 D) width = 100
π + 4 ≈ 14, length = 18
3) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches:
M(x) = 20x – x2. What rainfall produces the maximum number of mosquitoes?
A) 10 in. B) 0 in. C) 400 in. D) 20 in.
4) The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = –5p2 + 1530p, 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) $117,045 B) $234,090 C) $468,180 D) $936,360
5) A projectile is thrown upward so that its distance above the ground after t seconds is h = –13t2 + 494t.
After how many seconds does it reach its maximum height?
A) 19 sec B) 9 sec C) 28.5 sec D) 38 sec
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 – 30x + 670, where x is the number of videos rented daily. Find the
lowest cost to the nearest dollar.
A) $558 B) $220 C) $445 D) $783
7) A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the
developer has 348 feet of fencing and does not fence the side along the street, what is the largest area that
can be enclosed?
A) 15,138 ft2B) 30,276 ft2C) 7569 ft2D) 22,707 ft2
8) The quadratic function f(x) = 0.0036x2 – 0.43x + 36.86 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
,
24 years old B) 1960
,
49.7 years old
C) 1936, 49.7 years old D) 1953
,
36 years old
Page 69
9) A projectile is fired from a cliff 200 feet above the water at an inclination of 45° to the horizontal, with a
muzzle velocity of 370 feet per second. The height h of the projectile above the water is given by
h(x) = –32x2
(370)2 + x + 200, where x is the horizontal distance of the projectile from the base of the cliff. Find
the maximum height of the projectile.
A) 1269.53 ft B) 2139.06 ft C) 1069.53 ft D) 3408.59 ft
10) You have 84 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that
maximize the enclosed area.
A) 21 ft by 21 ft B) 42 ft by 42 ft C) 42 ft by 10.5 ft D) 23 ft by 19 ft
11) You have 116 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: 58 ft, width: 29 ft B) length: 87 ft, width: 29 ft
C) length: 58 ft, width: 58 ft D) length: 29 ft, width: 29 ft
12) The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the
function C(x) = 3x2 – 18x + 63. Find the number of automobiles that must be produced to minimize the
cost.
A) 3 thousand automobiles B) 6 thousand automobiles
C) 36 thousand automobiles D) 9 thousand automobiles
13) The profit that the vendor makes per day by selling x pretzels is given by the function
P(x) = –0.002x2 + 1.6x – 350. Find the number of pretzels that must be sold to maximize profit.
A) 400 pretzels B) 800 pretzels C) 0.8 pretzels D) –30 pretzels
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? Round values to the nearest thousandth.
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 – 22.126 B) B(x) = 0.0243x2 – 3.115x – 22.126
C) B(x) = –0.243x2 + 3.115x – 22.126 D) B(x) = –0.0243x2 + 3.115x + 22.126
Page 70
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. Round values to the nearest thousandth.
x (seconds after release) 1 2 3 4 5 6
y (distance in feet) 16 63 146 255 403 572
A) y = 15.536x2 + 2.936x – 3.400 B) y = –3.400x2 + 2.936x + 15.536
C) y = 15.536x2 + 2.936x + 3.400 D) y = 3.400x2 + 2.936x + 15.536
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? Round
values to the nearest thousandth.
Speed, s mph, M
20 18
30 20
40 23
50 25
60 28
70 24
80 22
A) M(s) = –0.006x2 + 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
4) The number of housing starts in one beachside community has increased over the last eight years. The
following data shows the number of housing starts over this period of time. Use a graphing calculator to
plot a scatter diagram. What is the quadratic function of best fit? Round values to the nearest thousandth.
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
Page 71
5) The number of housing starts in one beachside community has increased over the last eight years. The
following data shows the number of housing starts over this period of time. Use a graphing calculator to
plot a scatter diagram. What is the quadratic function of best fit? Round values to the nearest thousandth.
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). Find the quadratic function of best fit. Round values to
the nearest thousandth.
Advertising, x Total Revenue, R
25
28
31
32
34
39
40
45
6430
6432
6434
6434
6434
6431
6432
6420
A) R(x) = –0.091x2 + 5.952x + 6337.167 B) R(x) = –0.0242x2 + 7.139x + 6209.323
C) R(x) = –0.310x2 + 2.631x + 6128.455 D) R(x) = –0.015x2 + 4.536x + 6123.841
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 Tunney’s
Bicycle Shop. Using a graphing utility, find the quadratic function of best fit using coefficients rounded to
the nearest hundredth. Round values 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
Page 72
8) The following table shows the median number of hours of leisure time that Americans had each week in
various years.
Year 1988 1995 2002 2008 2012
Median # of Leisure hrs per Week 26.2 19.2 16.6 18.8 19.5
Use x = 0 to represent the year 1988. Using a graphing utility, determine the quadratic regression equation
for the data given. Round values to the nearest hundredth. 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) (4, 0)
x
-16 -12 -8 -4 4 8 12 16
y
16
12
8
4
-4
-8
-12
-16
(-2, 0) (4, 0)
A) {x|–2
x
4}; (–2
,
4) B) {x|–2≤x ≤4}; [–2
,
4]
C) {x|x ≤ –2 or x ≥ 4}; (–∞
,
–2] or [4
,
∞) D) {x|x
–2 or x >4}; (–∞
,
–2) or (4
,
∞)
2) g(x) ≤ 0
x
–16 -12 –8 –4 4 8 12 16
y
16
12
8
4
-4
-8
-12
-16
(-3, 0) (3, 0)
x
–16 -12 –8 –4 4 8 12 16
y
16
12
8
4
-4
-8
-12
-16
(-3, 0) (3, 0)
A) {x|x ≤ –3 or x ≥ 3}; (–∞
,
–3] or [3
,
∞) B) {x|–3≤ x ≤3}; [–3
,
3]
C) {x|–3
x
3}; (–3
,
3) D) {x|x
–3 or x >3}; (–∞
,
–3) or (3
,
∞)
Page 73
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, ∞)
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)
Page 74
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, ∞)
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 – 35 ≤ 0
A) [–5
,
7] B) (–∞
,
–5] C) [7
,
∞)D)(
–∞
,
–5] or [7
,
∞)
8) x2 + 5x + 4 > 0
A) (–∞
,
–4) or (–1
,
∞)B)(
–4
,
–1) C) (–∞
,
–4) D) (–1
,
∞)
9) x2 – 7x ≥ 0
A) (–∞
,
0] or [7
,
∞) B) [0, 7] C) (–∞
,
–7] or [0, ∞)D)[
–7
,
0]
10) x2 + 3x ≥ 0
A) (–∞
,
–3] or [0, ∞) B) [0, 3] C) (–∞
,
0] or [3
,
∞)D)[
–3
,
0]
11) x2 + 2x ≤ 0
A) [–2
,
0] B) [0, 2] C) (–∞
,
–2] or [0, ∞)D)(
–∞
,
0] or [2
,
∞)
Page 75
12) x2 – 3x ≤ 0
A) [0, 3] B) [–3
,
0] C) (–∞
,
–3] or [0, ∞)D)(
–∞
,
0] or [3
,
∞)
13) x2 – 36 > 0
A) (–∞
,
–6) or (6
,
∞)B)(
–6
,
6)
C) (–∞
,
–36) or (36
,
∞)D)(
–36
,
36)
14) x2 – 36 ≤ 0
A) [–6
,
6] B) (–∞
,
–6] or [6
,
∞)
C) (–∞
,
–36] or [36
,
∞)D)[
–36
,
36]
15) x2 + 5x ≥ –4
A) (–∞
,
–4] or [–1
,
∞)B)[
–4
,
–1] C) (–∞
,
–4] D) [–1
,
∞)
16) 4x2 – 20 < –11x
A) –4, 5
4B) 5
4, 4 C) –4, – 5
4D) – 5
4, 4
17) 64x2 + 9 < 48x
A) No real solution B) –∞, 3
8C) –∞, – 3
8D) – 3
8, ∞
18) 72(x2 – 1) > 17x
A) –∞, – 8
9 or 9
8, ∞B) – 8
9, 9
8C) –∞, – 9
8 or 8
9, ∞D) – 9
8, 8
9
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) = 30x2 – 30 and h(x) = 11x, then solve g(x) > h(x).
A) –∞, – 5
6 or 6
5, ∞B) – 6
5, 5
6C) – 5
6, 6
5D) –∞, – 6
5 or 5
6, ∞
22) If h(x) = x2 + 6x + 5 , solve h(x) > 0.
A) (–∞
,
–5) or (–1
,
∞)B)(
–5
,
–1) C) (–∞
,
–5) D) (–1
,
∞)
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(47 – 0.2x) dollars. The cost of
each calculator is $23. How many graphing calculators must be sold to make a profit (revenue – cost) of at
least $712.80?
A) {x∣54
x
66} B) {x∣24
x
36} C) {x∣55
x
53} D) {x∣56
x
64}
Page 76
25) A rock falls from a tower that is 240 ft high. As it is falling, its height is given by the formula h = 240 – 16t2.
How many seconds will it take for the rock to hit the ground (h = 0)?
A) 3.9 s B) 15.5 s C) 3600 s D) 15 s
26) A rock falls from a tower that is 137.2 m high. As it is falling, its height is given by the formula
h = 137.2 – 4.9t2. How many seconds will it take for the rock to hit the ground (h = 0)?
A) 5.3 s B) 11.7 s C) 3800 s D) 11.5 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 144 ft/sec, and the gorge is 320 ft deep, during what interval can the flare be seen?
(h = –16t2 + v0t + h0.)
A) 4
t
5B)8
t
9C)0
t
4 D) 12
t
13
28) A coin is tossed upward from a balcony 320 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 80 ft? (h = –16t2 + v0t + h0.)
A) 0 ≤ t ≤ 5B)0 ≤ t ≤1C)5
≤t ≤10 D) 4 ≤ t ≤5
29) If a rocket is propelled upward from ground level, its height in meters after t seconds is given by
h = –9.8t2 + 78.4t. During what interval of time will the rocket be higher than 147 m?
A) 3
t
5B)0
t
3C)5
t
6D)6
t
8
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 160 ft/sec, and the gorge is 336 ft deep, during what interval can the flare be seen?
(h = –16t2 + v0t + h0.)
A) 3
t
7B)6
t
10 C) 0
t
3D)9
t
13
31) A coin is tossed upward from a balcony 186 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 90 ft?
(h = –16t2 + v0t + h0.)
A) 0 ≤ t ≤ 3B)0 ≤ t ≤1C)3
≤t ≤6D)2
≤ t ≤3
32) If a rocket is propelled upward from ground level, its height in meters after t seconds is given by
h = –9.8t2 + 68.6t. During what interval of time will the rocket be higher than 98 m?
A) 2
t
5B)0
t
2C)5
t
4D)4
t
7
Page 77
Ch. 4 Linear and Quadratic Functions
Answer Key
4.1 Properties of Linear Functions and Linear Models
1 Graph 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
Page 81
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