Chapter 11 If they can cut the lawn in 5 hours working

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

50)

x3– 9x2+ 23x – 15 

0

50)

A)

[–5, –3]  [–1, )

B)

[1, 3] 

[5, )

C)

( , 1]  [5, )

D)

( , 1]  [3, 5]

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write

and factor the trinomial.

51)

x2–2

5x

51)

A)

1

25 ; x2–2

5x +1

25 =x –1

5

2

B)

2

25 ; x2–2

5x +2

25 =x –1

5

2

C)

1

25 ; x2–2

5x +1

25 =x +1

5

2

D)

4

25 ; x2–2

5x +4

25 =x –2

5

2

Determine whether the given quadratic function has a minimum value or maximum value. Then find the minimum or

maximum value and determine where it occurs.

52)

f(x) = – x2– 2x – 3

52)

A)

Maximum is – 1 at x = – 2.

B)

Minimum is – 1 at x = – 2.

C)

Minimum is – 2 at x = – 1.

D)

Maximum is – 2 at x = – 1.

Solve the problem.

53)

If g(x) = (x + 5)2, find all values of x for which g(x) =10.

53)

A)

±10

B)

±10

5

C)

–5±10

D)

5±10

Find the intercepts of the quadratic function.

54)

f(x) =2+3x + x2

54)

A)

x–intercepts: (–1, 0) and (–2, 0)

y–intercept: (0, 2)

B)

x–intercepts: (1, 0) and (2, 0)

y–intercept: (0, –2)

C)

x–intercepts: (1, 0) and (2, 0)

y–intercept: (0, 2)

D)

x–intercepts: (–1, 0) and (–2, 0)

y–intercept: (0, –2)

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

55)

f(x) =x2+ 4x – 7

55)

22

A)

vertex: –1

2, –12 1

4

x–intercepts: (–4, 0) and (3, 0)

y–intercept: (0, –12)

axis of symmetry: x = – 1

2

B)

vertex: (4, 0)

x–intercept: (4, 0)

y–intercept: (0, 7)

axis of symmetry: x = 4

C)

vertex: (–2, –11)

x–intercepts: (–2 ±11, 0)

y–intercept: (0, –7)

axis of symmetry: x = – 2

D)

vertex: (–2, 3)

x–intercepts: none

y–intercept: (0, 7)

axis of symmetry: x = – 2

23

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

56)

x2– 4x –3

56)

A)

(–, 1]

B)

[3, )

C)

[1, 3]

D)

(–, 1] 

[3, )

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

57)

{–9i, 9i}

A)

x2+81 = 0

B)

x2+18x +81 = 0

C)

x2–18x –81 = 0

D)

x2–81 = 0

Solve the equation by making an appropriate substitution.

58)

x4–40x2+144 = 0

58)

A)

{4, 36}

B)

{–2i, 2i, –6i, 6i}

C)

{2, 6}

D)

{–2, 2, –6, 6}

24

Complete the square for the binomial. Then factor the resulting perfect square trinomial.

59)

x2+ 8x

59)

A)

16; x2+ 8x +16 = (x +4)2

B)

8; x2+ 8x +8= (x +64)2

C)

64; x2+ 8x +64 = (x +8)2

D)

4; x2+ 8x +4= (x +16)2

Solve the problem.

60)

Suppose that an open box is to be made from a square sheet of cardboard by cutting out 4–inch

squares from each corner as shown and then folding along the dotted lines. If the box is to have a

volume of 400 cubic inches, find the original dimensions of the sheet of cardboard.

A)

10 in. by 10 in.

B)

20 in. by 20 in.

C)

10 in. by 210 in.

D)

18 in. by 18 in.

Complete the square for the binomial. Then factor the resulting perfect square trinomial.

61)

x2–2

3x

61)

A)

2

9; x2–2

3x +2

9=x –1

3

2

B)

1

9; x2–2

3x +1

9=x –1

3

2

C)

4

9; x2–2

3x +4

9=x –2

3

2

D)

1

9; x2–2

3x +1

9=x +1

3

2

Solve the equation by making an appropriate substitution.

62)

x –4x1/2 –32 = 0

62)

A)

{48}

B)

{128}

C)

{32}

D)

{64}

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

63)

f(x) = (x + 2)2+ 8

63)

A)

(8, –4)

B)

(8, –2)

C)

(–2, 8)

D)

(–8, 2)

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

imaginary solutions in the form a +

bi.

64)

x2–20x +100 =36

64)

A)

{–26, 46}

B)

{–16, –4}

C)

{16}

D)

{4, 16}

26

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

65)

x2– 5x – 14  0

65)

A)

(–, –2]

B)

[7, )

C)

[–2, 7]

D)

(–, –2]  [7, )

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

imaginary solutions in the form a +

bi.

66)

13x2–2= 0

66)

A)

±13

2

B)

±26

13

C)

±13

26

D)

±2

13

Find the distance between the pair of points. Give an exact answer.

67)

(0, –2) and (3, –2)

A)

2 units

B)

13 units

C)

9 units

D)

3 units

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

68)

{3 +5, 3–5}

68)

A)

x2+ 4 = 0

B)

x2– 4 = 0

C)

x2–6x + 4 = 0

D)

x2+6x – 4 = 0

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

69)

f(x) =6x2+ 12x + 2

69)

A)

(2, 50)

B)

(–2, 14)

C)

(–1, –4)

D)

(1, 20)

Use the quadratic formula to solve the equation.

70)

x(x + 6) =5

A)

{–3±14}

B)

{–3±2}

C)

{3 ±2}

D)

{3 ±14}

Solve the equation by making an appropriate substitution.

71)

y –10

y

2– 6 y –10

y–27 = 0

71)

A)

{– 5, 2}

B)



C)

{– 5, – 1, 2, 10}

D)

{–3, 9}

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

72)

f(x) = (x – 4)2– 4

72)

A)

(–4, 0)

B)

(4, 4)

C)

(4, –4)

D)

(0, –4)

Solve the equation by making an appropriate substitution.

73)

2x1/2 – 15x1/4 – 27 = 0

73)

A)

9, –3

2

B)

{–9, –3}

C)

6561, 81

16

D)

{6561}

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

74)

f(x) = (x + 7)2– 9

74)

A)

(7, –9)

B)

(7, 9)

C)

(–7, 9)

D)

(–7, –9)

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

75)

(x – 9)2+49 = 0

75)

A)

{–9±7i}

B)

{9 ±7i}

C)

{2, 16}

D)

{–16, –2}

29

Solve the problem.

76)

The cost in millions of dollars for a company to manufacture x thousand automobiles is given by

the function C(x) =3x2– 12x +32. Find the number of automobiles that must be produced to

minimize the cost.

A)

20 thousand automobiles

B)

2 thousand automobiles

C)

4 thousand automobiles

D)

6 thousand automobiles

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

77)

x2– 16x +64 > 0

77)

A)

(–, 8) 

(8, )

B)

(–, )

C)

(–, 8)

D)

(8, )

Solve the problem.

78)

If f(x) = (x – 3)2 , find all values of x for which f(x) =4.

78)

A)

7

B)

1, 5

C)

2, –2

D)

–5, 1

79)

The hypotenuse of a right triangle is 5 feet long. One leg of the triangle is 3 feet longer then the

other leg. Find the perimeter of the triangle.

A)

(41 –5) ft

B)

3

2+41

2 ft

C)

(41 +5) ft

D)

–3

2+41

2 ft

80)

Shelly can cut a lawn with a riding mower in 3 hours less time than it takes William to cut the

lawn with a push mower. If they can cut the lawn in 5 hours working together find how long to

the nearest tenth of an hour it takes for William to cut the lawn alone.

A)

8.8 hr

B)

11.7 hr

C)

11.8 hr

D)

8.7 hr

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

81)

f(x) = (x + 3)2+ 4

81)

A)

y =4

B)

x =3

C)

y = – 4

D)

x = – 3

Solve the equation by making an appropriate substitution.

82)

x–2+ 6x–1+5= 0

82)

A)

–1

5, –1

B)

{–1, –5}

C)

{1, 5}

D)

1

5, 1

31

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

83)

f(x) = 11(x –4)2+ 8

83)

A)

x = – 4

B)

x =8

C)

x =4

D)

x = 11

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

84)

– 1, –5

2 and 3, – 3

84)

A)

2, –11

2

B)

– 2, 1

4

C)

1, –11

4

D)

2, –1

4

Solve the problem.

85)

You have 300 feet of fencing to enclose a rectangular region. What is the maximum area?

A)

5621 sq ft

B)

22,500 sq ft

C)

90,000 sq ft

D)

5625 sq ft

Solve the quadratic equation by completing the square.

86)

x2+ 5x – 5 = 0

86)

A)

{–5±3 5}

B)

5±3 5

2

C)

–5±3 5

2

D)

–5+3 5

2

32