Chapter 11 A developer wants to enclose a rectangular grassy lot

Exam

Name___________________________________

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

question.

Match the graph with its function using the x–intercepts.

1)

A)

f(x) =x1/2 + 2x1/4 + 1

B)

f(x) =x1/2 +14x1/4 –15

C)

f(x) =x1/2 + 2x1/4 – 1

D)

f(x) =x1/2 –14x1/4 –15

2)

A)

f(x) =x–2–x–1+ 2

B)

f(x) =x–2+x–1+ 2

C)

f(x) =x–2+x–1– 2

D)

f(x) =x–2–x–1– 2

3)

A)

f(x) =2(x – 2)2– 3(x – 2) – 5

B)

f(x) =2(x + 2)2– 3(x + 2) – 5

C)

f(x) =2(x – 2)2+ 3(x – 2) – 5

D)

f(x) =2(x + 2)2+ 3(x + 2) – 5

The graph of a quadratic function is given. Choose the function’s equation.

4)

A)

f(x) =x2–4x +4

B)

f(x) =x2–2

C)

f(x) =x2+4x +4

D)

f(x) =x2+2

Match the graph with its function using the x–intercepts.

5)

A)

f(x) =x1/3 –10x1/6 +11

B)

f(x) =x1/3 –10x1/6 –11

C)

f(x) =x1/3 +10x1/6 –11

D)

f(x) =x1/3 +10x1/6 +11

The graph of a quadratic function is given. Choose the function’s equation.

6)

A)

f(x) = – x2–2x –1

B)

f(x) = – x2+2x +1

C)

f(x) = – x2–1

D)

f(x) = – x2+1

Match the graph with its function using the x–intercepts.

7)

A)

f(x) = 6x–2– 5x–1+ 1

B)

f(x) = 6x–2– 5x–1– 1

C)

f(x) = 6x–2+ 5x–1– 1

D)

f(x) = 6x–2+ 5x–1+ 1

The graph of a quadratic function is given. Choose the function’s equation.

8)

A)

f(x) =x2–2x +1

B)

f(x) =x2–1

C)

f(x) =x2+1

D)

f(x) =x2+2x +1

Match the graph with its function using the x–intercepts.

9)

A)

f (x) =x4+ 2x2– 1

B)

f (x) =x4– 2x2– 1

C)

f (x) =x4– 2x2+ 1

D)

f (x) =x4+ 2x2+ 1

The graph of a quadratic function is given. Choose the function’s equation.

10)

A)

f(x) =(x +1)2+1

B)

f(x) =(x –1)2+1

C)

f(x) =(x –1)2–1

D)

f(x) =(x +1)2–1

11)

A)

f(x) =x2–4x +4

B)

f(x) =x2–2

C)

f(x) =x2+2

D)

f(x) =x2+4x +4

Match the graph with its function using the x–intercepts.

12)

A)

f(x) =x4–25x2+144

B)

f(x) =x4–25x2+12

C)

f(x) =x4+25x2+144

D)

f(x) =x4+25x2–12

13)

A)

f(x) =(x + 1)2+ 4(x + 1) + 4

B)

f(x) =(x + 1)2+ 2(x + 1) + 1

C)

f(x) =(x + 1)2– 4(x + 1) + 4

D)

f(x) =(x + 1)2– 2(x + 1) + 1

The graph of a quadratic function is given. Choose the function’s equation.

14)

A)

f(x) =(x –1)2–1

B)

f(x) =(x +1)2–1

C)

f(x) =(x –1)2+1

D)

f(x) =(x +1)2+1

15)

A)

f(x) = – x2+2x +1

B)

f(x) = – x2–2x –1

C)

f(x) = – x2+1

D)

f(x) = – x2–1

16)

A)

f(x) =(x –2)2+2

B)

f(x) =(x –2)2–2

C)

f(x) =(x +2)2–2

D)

f(x) =(x +2)2+2

17)

A)

f(x) =(x +1)2–1

B)

f(x) =(x +1)2+1

C)

f(x) =(x –1)2–1

D)

f(x) =(x –1)2+1

18)

A)

f(x) =x2+1

B)

f(x) =x2+2x +1

C)

f(x) =x2–1

D)

f(x) =x2–2x +1

Match the graph with its function using the x–intercepts.

19)

A)

f(x) =x–2+ 2x–1+ 3

B)

f(x) =x–2– 2x–1+ 3

C)

f(x) =x–2+ 2x–1– 3

D)

f(x) =x–2– 2x–1– 3

20)

A)

f(x) =x4+5x2–4

B)

f(x) =x4–5x2+4

C)

f(x) =x4–5x2–4

D)

f(x) =x4+5x2+4

Solve the rational inequality and graph the solution set on a real number line.

21)

x

x +4 2

21)

A)

[–8, –4)

B)

(–

, –4)  [0, 

)

C)

(–

, –8]  (–4, 

)

D)

(–4, 8]

Solve.

22)

Imelda inherited $20,000 and invested it in a mutual fund for two years. At the end of the two

years, her investment had grown to $22,898. Determine the annual compound interest rate that

would yield this amount of money. Use the compound interest formula A = P(1 + r)t.

A)

0.7%

B)

7%

C)

0.07%

D)

70%

Write a quadratic equation in standard form with the given solution set.

23)

{4, 1}

A)

x2–4x +5= 0

B)

x2+5x +4= 0

C)

x2–5x +4= 0

D)

x2+4x +5= 0

Solve the problem.

24)

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

developer has 344 feet of fencing and does not fence the side along the street, what is the largest

area that can be enclosed?

A)

14,792 sq ft

B)

22,188 sq ft

C)

29,584 sq ft

D)

7396 sq ft

25)

The daily profit in dollars of a specialty cake shop is described by the function

P(x) = – 6x2+312x –2880, where x is the number of cakes prepared in one day. The maximum

profit for the company occurs at the vertex of the parabola. How many cakes should be prepared

per day in order to maximize profit?

A)

676 cakes

B)

4056 cakes

C)

26 cakes

D)

52 cakes

Find the range of the quadratic function.

26)

f(x) = (x + 4)2– 8

26)

A)

( , –4]

B)

[–4, 

)

C)

( , –8]

D)

[–8, 

)

Without solving the given quadratic equation, determine the number and type of solutions.

27)

x2+ 7x – 7 = 0

27)

A)

two real rational solutions

B)

one (repeated) real rational solution

C)

two real irrational solutions

D)

two imaginary solutions

Solve the problem.

28)

April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is

32 feet high. The height of the arrow is given by the function h(t) = – 16t2+64t +32, where t is the

time is seconds. What is the maximum height of the arrow?

A)

96 ft

B)

32 ft

C)

28 ft

D)

64 ft

Solve the equation by making an appropriate substitution.

29)

x –9 x +18 = 0

29)

A)

{–3, 3, –6, 6}

B)

{–3, 3, –6, 6}

C)

{9, 36}

D)

{3, 6}

13

Solve the formula for the specified variable. Assume all variables represent nonnegative numbers. If possible, simplify

radicals and rationalize denominators.

30)

V =r2h for r

30)

A)

r =Vh

B)

r =V

2h

C)

r =V

h

D)

r =Vh

h

Solve the polynomial inequality and graph the solution set on a number line.

31)

x3+ 5x2+ 8x + 16 

0

31)

A)

[–4, 

)

B)

( , –4]  [4, 

)

C)

( , –4]  [1, 4]

D)

( , –4]

Solve the problem.

32)

Among all pairs of numbers whose sum is 42, find a pair whose product is as large as possible.

A)

23 and 19

B)

41 and 1

C)

10.5 and 10.5

D)

21 and 21

Solve the equation by making an appropriate substitution.

33)

x4–40x2+144 = 0

33)

A)

{4, 36}

B)

{–2, 2, –6, 6}

C)

{2, 6}

D)

{–2i, 2i, –6i, 6i}

Find the midpoint of the line segment with the given end points.

34)

(3, 6) and (9, 4)

A)

(–6, 2)

B)

(12, 10)

C)

6, 5

D)

– 3, 1

Solve the formula for the specified variable. Assume all variables represent nonnegative numbers. If possible, simplify

radicals and rationalize denominators.

35)

F =

Gm1m2

d2 for d

35)

A)

d =Gm1m2F

B)

d =

Gm1m2

2F

C)

d =

Gm1m2F

F

D)

d =

Gm1m2

F

Use the quadratic formula to solve the equation.

36)

x2+ 4x + 29 = 0

36)

A)

{–2±25i}

B)

{–2±5i}

C)

{–2+5i}

D)

{–7, 3}

Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.

15

37)

f(x) =3–x2+ 2x

37)

A)

vertex: (– 1, 4)

x–intercepts: (–3, 0) and (1, 0)

y–intercept: (0, 3)

axis of symmetry: x = – 1

B)

vertex: (1, 4)

x–intercepts: (–1, 0) and (3, 0)

y–intercept: (0, 3)

axis of symmetry: x =1

C)

vertex: (1, – 4)

x–intercepts: (–1, 0) and (3, 0)

y–intercept: (0, 3)

axis of symmetry: x =1

D)

vertex: (1, 4)

x–intercepts: (–3, 0) and (1, 0)

y–intercept: (0, 3)

axis of symmetry: x =1

16

Find the axis of symmetry of the parabola defined by the given quadratic function.

38)

f(x) = (x + 3)2– 7

38)

A)

x =3

B)

x = – 3

C)

x = – 7

D)

x =7

Solve the formula for the specified variable. Assume all variables represent nonnegative numbers. If possible, simplify

radicals and rationalize denominators.

39)

V =s2h

3 for s

39)

A)

s =3Vh

B)

s =3Vh

h

C)

s =3V

h

D)

s =3V

2h

Solve the equation by making an appropriate substitution.

40)

x4– 31x2–180 = 0

40)

A)

{–5, 5, –6i, 6i}

B)

{–36, 5}

C)

{6, i 5}

D)

{–6, 6, –i 5, i 5}

Use the quadratic formula to solve the equation.

41)

4x2= – 8x – 2

41)

A)

–2±6

2

B)

–2±2

2

C)

–8±2

2

D)

–2±2

8

17

Solve the problem.

42)

A rain gutter is made from sheets of aluminum that are 18 inches wide by turning up the edges to

form right angles. Determine the depth of the gutter that will maximize its cross–sectional area

and allow the greatest amount of water to flow.

A)

4 in.

B)

5.5 in.

C)

4.5 in.

D)

5 in.

Use the discriminant to determine the number and type of solutions for the given equation.

43)

x2+ 3x + 2 = 0

43)

A)

one (repeated) real rational solution

B)

two real rational solutions

C)

two real irrational solutions

D)

two imaginary solutions

Find the intercepts of the quadratic function.

44)

f(x) = – x2– 2x +8

44)

A)

x–intercepts: (–4, 0) and (2, 0)

y–intercept: (0, 8)

B)

x–intercepts: (–2, 0) and (4, 0)

y–intercept: (0, 8)

C)

x–intercepts: (–2, 0) and (4, 0)

y–intercept: (0, –8)

D)

x–intercepts: (–4, 0) and (2, 0)

y–intercept: (0, –8)

Solve the equation by the method of your choice. Simplify solutions, if possible.

45)

x2+ 18x + 58 = 0

45)

A)

{9 ±23}

B)

{–18 ±58}

C)

{9 ±58}

D)

{–9±23}

18

Solve the equation by the square root property. If possible, simplify radicals or rationalize denominators. Express

imaginary solutions in the form a +

bi.

46)

x –1

2

2=9

4

46)

A)

{–2, 1}

B)

{–4, 2}

C)

{–1, 2}

D)

{–2, 4}

Write a quadratic equation in standard form with the given solution set.

47)

{–2, –7}

A)

x2+14x – 9 = 0

B)

x2+9x +14 = 0

C)

x2–14x – 9 = 0

D)

x2– 9x +14 = 0

48)

{–5, 1}

A)

x2+ 4x – 5 = 0

B)

x2+ 5x – 4 = 0

C)

x2– 4x – 5 = 0

D)

x2– 5x – 4 = 0

Sketch the graph of the quadratic function. Identify the vertex, intercepts, and the equation for the axis of symmetry.

49)

f(x) =2x2– 8x + 9

49)

19

A)

vertex: (2, 1)

x–intercepts: none

y–intercept: (0, 9)

axis of symmetry: x =2

B)

vertex (2, 1)

x–intercepts: none

y–intercept: 0, 3

axis of symmetry: x =2

C)

vertex (–2, 1)

x–intercepts: none

y–intercept 0, 3

axis of symmetry: x = – 2

D)

vertex (–2, 1)

x–intercepts: none

y–intercept (0, 9)

axis of symmetry: x = – 2

20