Extra Practice Skills Practice Chapter 8 - MATH WIZARDS

Extra Practice Chapter 8

Lesson

8-1

Skills Practice

Tell whether each function is quadratic. Explain.

1. y + 4x 2 = 2x - 3

2. 4x - y = 3

4.

5.

x

-6

-4

-2

0

2

y

-5

-6

-4

2

11

3. 3x 2 - 4 = y + x

x

0

1

2

3

4

y

-5

-5

-3

1

7

Tell whether the graph of each quadratic function opens upward or downward.

Then use a table of values to graph each function.

2 x2

6. y = -3x 2

7. y = _

8. y = x 2 + 2

9. y = -4x 2 + 2x

3

Identify the vertex of each parabola. Then find the domain and range.

10.

11.

y

12.

y

2

8

2

x

x

-4

2

-2

6

2

-2

y

-2

4

-4

2

-2

x

2

Lesson

8-2

4

6

2

4

Find the zeros of each quadratic function and the axis of symmetry of each

parabola from the graph.

13.

8

14.

y

2

15.

y

2

y

x

6

0

-2

2

4

x

-2

0

4

-2

-2

2

-4

-4

x

-4

-2

0

Find the vertex.

16. y = 3x 2 - 6x + 2

Lesson

8-3

8

2

4

17. y = -2x 2 + 8x - 3

18. y = x 2 + 2x - 4

Graph each quadratic function.

19. y = x 2 - 4x + 1

20. y = -x 2 - x + 4

21. y = 3x 2 - 3x + 1

22. y - 2 = 2x 2

24. y - 4 = x 2 + 2x

23. y + 3x 2 = 3x - 1

Lesson

Order the functions from narrowest to widest.

8-4

25. f (x) = 2x 2, g(x) = -4x 2, h(x) = -x 2

1 x 2, h(x) = -2x 2

26. f (x) = 3x 2, g(x) = _

2

1 x2

27. f (x) = 4x 2, g(x) = x 2, h(x) = - _

28. f (x) = 2x 2, g(x) = 5x 2, h(x) = -3x 2

4

Compare the graph of each function with the graph of f (x) = x 2.

1 x2

29. g(x) = 2x 2 - 2

30. g(x) = - _

31. g(x) = -3x 2 + 1

2

EPS16

Extra Practice Chapter 8

Lesson

8-5

Lesson

8-6

Skills Practice

Solve each quadratic equation by graphing the related function.

32. x 2 - x - 2 = 0

33. x 2 - 2x + 8 = 0

34. 2x 2 + 4x - 6 = 0

35. 2x 2 + 9x = -4

36. 2x 2 + 3 = 0

37. 2x 2 - 2x - 12 = 0

38. 3x 2 = -3x + 6

39. x 2 = 4

40. 2x 2 + 6x - 20 = 0

Use the Zero Product Property to solve each equation. Check your answer.

41. (x + 3)(x - 2) = 0

42. (x - 4)(x + 2) = 0

43. (x)(x - 4) = 0

44. (2x + 6)(x - 2) = 0

45. (3x - 1)(x + 3) = 0

46. (x)(2x - 4) = 0

Solve each quadratic equation by factoring. Check your answer.

47. x 2 + 5x + 6 = 0

48. x 2 - 3x - 4 = 0

49. x 2 + x - 12 = 0

50. x 2 + x - 6 = 0

Lesson

8-7

Lesson

8-8

Lesson

8-9

51. x 2 - 6x + 5 = 0

52. x 2 + 4x - 12 = 0

Solve using square roots. Check your answer.

53. x 2 = 169

54. x 2 = 121

55. x 2 = 289

56. x 2 = -64

57. x 2 = 81

58. x 2 = -441

59. 4x 2 - 196 = 0

60. 0 = 3x 2 - 48

61. 24x 2 + 96 = 0

Solve. Round to the nearest hundredth.

62. 4x 2 = 160

63. 0 = 3x 2 - 66

64. 250 - 5x 2 = 0

65. 0 = 9x 2 - 72

67. 6x 2 = 78

66. 48 - 2x 2 = 42

Complete the square to form a perfect-square trinomial.

68. x 2 - 8x +

69. x 2 + x +

70. x 2 + 10x +

71. x 2 - 5x +

73. x 2 - 7x +

72. x 2 + 6x +

Solve by completing the square.

74. x 2 + 6x = 91

75. x 2 + 10x = -16

76. x 2 - 4x = 12

77. x 2 - 8x = -12

78. x 2 - 12x = -35

79. -x 2 - 6x = 5

80. -x 2 - 4x + 77 = 0

81. -x 2 = 10x + 9

82. -x 2 + 63 = -2x

Solve using the quadratic formula.

83. x 2 + 3x - 4 = 0

84. x 2 - 2x - 8 = 0

85. x 2 + 2x - 3 = 0

86. x 2 - x - 10 = 0

88. 2x 2 + 3x - 3 = 0

87. 2x 2 - x - 4 = 0

Find the number of real solutions of each equation using the discriminant.

89. x 2 + 4x + 1 = 0

90. 2x 2 - 3x + 2 = 0

91. x 2 - 5x + 2 = 0

92. 2x 2 - 4x + 2 = 0

Lesson

8-10

93. x 2 + 2x - 5 = 0

Solve each system of equations.

?y = -x - 1

? y = -3x

95. ?

96. ?

?y = x 2 - 3

? y = x2 + 2

?y = -x + 6

98. ?

?y = x 2 - x + 2

?y = x - 1

99. ?

? y = x 2 - 5x + 3

EPS17

94. 2x 2 - 2x - 3 = 0

?y = 3x - 2

97. ?

? y = -3x 2 + 4

?y = 2x - 7

100. ?

? y = x 2 - 2x - 4

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