Alg1 RBC Answers A

Answers

46.

-8z8

+ z3

+

3 z2; trinomial 8

47. 2g + 3

48. -3h - 5

49. - v2 + 11v - 17 51. -2x - 15

50. -12t3 + 5t 2 - 5t + 7 52. 13y + 38

53. - x2 + 7 x - 17

54. 7w4 - 3w2 - 10w - 7

55. x2 - 2x - 15

56. y2 - 3 y - 10

57. n2 - 13n + 30

59. a. 2x2 + 25x + 50 b. 875 ft2

60. x2 + 8x + 16

58. 2r2 + 13r - 45 61. 9 y2 - 30 y + 25

62. 49x2 + 42xy + 9 y2 63. w2 - 4

64. 4m2 - 16m + 16

66. a. 9x2 + 12x + 4 b. 121 square units

67. -5, 3

65. 81h2 - 4t2 68. -5, 2

69.

8 7

71. 0, 3

73. 0, 3

70.

-

2 5

,

2 5

72.

-

2 3

,

0

74. ( y + 2)( y + 5)

75. (x + 4)(x + 2)

76. (w + 9)(w + 2)

77. (x - 4)(x - 2)

78. (d - 3)(d - 4)

79. (z - 10)(z - 2)

80. (m + 5)(m - 3)

81. (z + 6)(z - 4)

82. (x - 11)(x + 1)

83. -4, -1

84. -6, 9

85. 2(x + 5)(x + 6)

86. 5( y + 1)( y + 4)

87. 6(w + 10)(w + 1) 88. (2t + 1)(t + 2)

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89. (3u - 2)(u - 2)

90. -(2z + 5)(3z + 5)

91. (x - 4)(4x - 1)

92. (r - 7)(4r - 7)

93. (5g - 3)(g - 3)

94. 5 sec

95. (x + 10)(x - 10) 96. (h + 6)(h - 6)

97. (3b + 5)(3b - 5)

98. (k + 4)2

99. (a - 15)2

101. -8, 8

100. (10g + 9)2

102. 7, 7 repeated root

( ) 103. 5x2 + 6 (5x + 1)

( ) 104. 4y2 - 3 (7 y + 4)

( ) 105. 8w2 + 1 (w - 8)

( ) 106. 3x2 - 2 (5x + 7)

Chapter 8 8.1 Start Thinking Sample answer:

Quadratic equation

Shape

Relationship to y = x2

y = 2x2

U-Shape

slightly narrowed

y

=

1 x2 2

y = -x2

y = (2x)2

U-Shape slightly widened

upside-down U-Shape

U-Shape

reflection in the x-axis

moderately narrowed

The value of the coefficient of the x2 -term determines how wide or narrow the graph is, and if negative, shows a reflection in the x-axis; Sample answer: The graph of y = - x2 looks the most different because it is

reflected in the y-axis.

Algebra 1 Answers

A87

Answers

8.1 Warm Up

1.

y

2

-2 -2

2x

2.

y

5

3

-3

2x

3.

y

2

-3

2x

-3

4.

y

4

-2

2x

5.

y

2

-2 -2

2x

A88

Algebra 1 Answers

6.

-2

y x

2

-2

-5

8.1 Cumulative Review Warm Up

1. x2 - 4x + 4

2. z2 + 4z - 12

3. g 2 + 9g + 8

4. y2 - 10 y + 21

5. 4m2 - 40m

8.1 Practice A

1.

y

6. x2 - 5x + 4

10

6

-2

2x

vertical stretch by factor of 4; both open up; same vertex; same axis of symmetry

2.

y

2

-2 -2

2x

vertical stretch by factor of 1.5; both open up; same vertex; same axis of symmetry

3.

y

2

-2 -2

2x

vertical shrink by factor of 1; both open up; same 3

vertex; same axis of symmetry

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Answers

4.

-2

y 2x

-6 -10

vertical stretch by factor of 3; reflection in the x-axis; same vertex; same axis of symmetry

5.

-2

y 2x

-4

-8

-12

vertical

stretch by factor of

5 2

;

reflection in the

x-axis; same vertex; same axis of symmetry

6.

y

2

-2 -2

2x

vertical shrink by factor of 0.5; reflection in the x-axis; same vertex; same axis of symmetry

7.

8

-6

6

0

reflection in the x-axis; same vertex; same axis of symmetry

8.

0

-6

6

-8

wider; vertical shrink by factor of 0.5; same vertex; same axis of symmetry

9.

0

-6

6

-8

much wider; vertical shrink by factor of 0.05; same vertex; same axis of symmetry

10. a. -400 x 400; The vertex is at x = 0, so 400 feet in both directions.

b.

150

-400

400

-400

height: 200 ft 11. yes; If x = 0, then y = 0 regardless the value

of a. 12. never; same width of a 13. sometimes; true when a > 0

14. always; f (- x) = ax2 = g (x); d = a

15. never; - f (x) = - ax2 = g (x); d = - a

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Algebra 1 Answers

A89

Answers

8.1 Practice B

1.

y

30

20

10

-2

2x

vertical stretch by factor of 7; both open up; same vertex; same axis of symmetry

2.

y

2

-2 -2

2x

vertical shrink by factor of 0.25; both open up; same vertex; same axis of symmetry

3.

y

12

8

4

-2

2x

vertical stretch by factor of

7 2

;

both

open

up;

same

vertex; same axis of symmetry

4.

-2

y 2x

-4

-8

-12

vertical stretch by factor of 5; reflection in the 3

x-axis; same vertex; same axis of symmetry

5.

y

2

-2 -2

2x

vertical shrink by factor of

3 4

;

reflection

in the

x-axis; same vertex; same axis of symmetry

6.

y

2

-2 -2

2x

vertical shrink by factor of 0.4; reflection in the x-axis; same vertex; same axis of symmetry

7. The vertical stretch by a factor of 2 was not taken into account.

y

2

y = x2

-2 -3

2x

y = -2x2

The graphs have the same vertex and the same axis of symmetry. The graph of y = - 2x2 is a

reflection in the x-axis of the graph of y = x2 , and a vertical stretch by a factor of 2.

A90

Algebra 1 Answers

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Answers

8. a. -450 x 450; The vertex is at x = 0, so 450 feet in both directions.

b.

y

300

200

100

-350

-200

-100

200 350 x

-200

-300

-400

-500

-600

-700

-800

height: 675 ft

9. Because the parabola opens down, the y-value of the vertex is the largest y-value.

10.

a.

a

=

1 - 9

b. not possible; When a > 0, the parabola has a range greater than or equal to zero.

8.1 Enrichment and Extension 1. Sample answer: y = 2x2 - 6

2. Sample answer:

y

4

-2

2x

6.

y

-6 -10

4x

7. The x-intercepts of the graph are at -5 and 5.

8. x = ?4

9.

y

-6

6x

-6

10. The x-intercepts of the graph are at 4 and -4.

11. no solution

12.

y

12

8

-2

2x

13. The graph does not intersect the x-axis.

14. You cannot solve the equation because you cannot square a number and get a negative number. This is why the graph does not show roots for the equation.

8.1 Puzzle Time IN A TREE TRUNK

3. (0, -6) is a minimum. 4. domain: (-, ), range: [-6, )

5. x = ?5

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Algebra 1 Answers

A91

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