Alg1 RBC Answers A -...

Answers

Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers

A87

46. 8 3 238 ;

8z z zπ− + + trinomial

47. 2 3g + 48. 3 5h− −

49. 2 11 17v v− + − 50. 3 212 5 5 7t t t− + − +

51. 2 15x− − 52. 13 38y +

53. 2 7 17x x− + −

54. 4 27 3 10 7w w w− − −

55. 2 2 15x x− − 56. 2 3 10y y− −

57. 2 13 30n n− + 58. 22 13 45r r+ −

59. a. 22 25 50x x+ +

b. 875 ft2

60. 2 8 16x x+ + 61. 29 30 25y y− +

62. 2 249 42 9x xy y+ + 63. 2 4w −

64. 24 16 16m m− + 65. 2 281 4h t−

66. a. 29 12 4x x+ +

b. 121 square units

67. 5, 3− 68. 5, 2−

69. 8

7 70.

2 2,

5 5−

71. 0, 3 72. 2

, 03

−

73. 0, 3 74. ( )( )2 5y y+ +

75. ( )( )4 2x x+ + 76. ( )( )9 2w w+ +

77. ( )( )4 2x x− − 78. ( )( )3 4d d− −

79. ( )( )10 2z z− − 80. ( )( )5 3m m+ −

81. ( )( )6 4z z+ − 82. ( )( )11 1x x− +

83. 4, 1− − 84. 6, 9−

85. ( )( )2 5 6x x+ + 86. ( )( )5 1 4y y+ +

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

89. ( )( )3 2 2u u− − 90. ( )( )2 5 3 5z z− + +

91. ( )( )4 4 1x x− − 92. ( )( )7 4 7r r− −

93. ( )( )5 3 3g g− − 94. 5 sec

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

97. ( )( )3 5 3 5b b+ − 98. ( )24k +

99. ( )215a − 100. ( )2

10 9g +

101. 8, 8−

102. 7, 7 repeated root

103. ( )( )25 6 5 1x x+ +

104. ( )( )24 3 7 4y y− +

105. ( )( )28 1 8w w+ −

106. ( )( )23 2 5 7x x− +

Chapter 8 8.1 Start Thinking

Sample answer:

The value of the coefficient of the 2x -term determines how wide or narrow the graph is, and if negative, shows a reflection in the x-axis; Sample answer: The graph of

2y x= − looks the most different because it is

reflected in the y-axis.

Quadratic equation Shape

Relationship to 2=y x

22y x= U-Shape slightly

narrowed

21

2y x= U-Shape slightly widened

2y x= − upside-down U-Shape

reflection in the x-axis

( )22y x= U-Shape

moderately narrowed

Answers

Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A88

8.1 Warm Up

1.

2.

3.

4.

5.

6.

8.1 Cumulative Review Warm Up

1. 2 4 4x x− + 2. 2 4 12z z+ −

3. 2 9 8g g+ + 4. 2 10 21y y− +

5. 24 40m m− 6. 2 5 4x x− +

8.1 Practice A

1.

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

2.

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

3.

vertical shrink by factor of 1

;3

both open up; same

vertex; same axis of symmetry

y

3

5

2−3 x

y2

−3 2 x

−3

y

4

−2 2 x

y

2

−2 2 x

−2

y

−2 2

x

−2

−5

y

6

10

−2 2 x

y

−2

2

−2 2 x

y

2

−2 2 x

−2

y

2

−2 2 x

−2

Answers


A89

4.

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

5.

vertical stretch by factor of 5

;2

reflection in the

x-axis; same vertex; same axis of symmetry

6.

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

7.

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

8.

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

9.

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

10. a. 400 400;x− ≤ ≤ The vertex is at 0,x = so

400 feet in both directions.

b.

height: 200 ft

11. yes; If 0,x = then 0y = regardless the value

of a.

12. never; same width of a

13. sometimes; true when 0a >

14. always; ( ) ( )2 ;f x ax g x d a− = = =

15. never; ( ) ( )2 ;f x ax g x d a− = − = = −

y

−2 2 x

−10

−6

y

−2 2 x

−12

−4

−8

y

2

−2 2 x

−2

−60

8

6

−6

−8

06

−6

−8

06

−400

−400

150

400

Answers


8.1 Practice B

1.

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

2.

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

3.


;2

both open up; same

vertex; same axis of symmetry

4.


;3

reflection in the


5.

vertical shrink by factor of 3

;4

reflection in the


6.

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.

The graphs have the same vertex and the same axis of symmetry. The graph of 22y x= − is a

reflection in the x-axis of the graph of 2 ,y x= and

a vertical stretch by a factor of 2.

y30

20

10

−2 2 x

y

−2

2

−2 2 x

y

4

8

12

−2 2 x

y

−4

−8

−12

−2 2 x

y

2

−2 2 x

−2

y

2

−2 2 x

−2

y

−3

2

−2 2 x

y = −2x2

y = x2

Answers


A91

8. a. 450 450;x− ≤ ≤ The vertex is at 0,x = so

450 feet in both directions.

b.

height: 675 ft

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

10. a. 1

9a = −

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

8.1 Enrichment and Extension

1. Sample answer: 22 6y x= −

2. Sample answer:

3. ( )0, 6− is a minimum.

4. domain: ( ), ,−∞ ∞ range: [ )6,− ∞

5. 5x = ±

6.

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

8. 4x = ±

9.

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

11. no solution

12.

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

y

100

200

300

−200−350 200 350 x

−100

−200

−300

−400

−500

−600

−800

−700

y

4

−2 2 x

y

4−6

−10

x

y

6−6

−6

x

y

8

12

−2 2 x

Answers


8.2 Start Thinking

The y-intercept of the equation is .y mx b b= + In

the equation ,y mx= the y-intercept is the origin

because 0.b = The graph of the function y mx= is

translated up when the y-intercept is positive and translated down when the y-intercept is negative.

Similar to the y-intercept in a linear equation, the value of c in a quadratic equation translates the graph up when c is positive and down when c is negative. The graph of the equation 2y ax= − is the graph of 2y x=reflected in the x-axis and vertically stretched or shrunk. The graph of the equation of 2y x c= − is the graph

of 2y x= translated down c units.

8.2 Warm Up

1. ( ) ( )4, 0 , 0, 4 2. ( ) ( )11, 0 , 0, 11−

3. ( ) ( )6.5, 0 , 0, 13− 4. ( ) ( )0.5, 0 , 0, 0.2−

5. ( ) ( )2, 0 , 0, 12− 6. ( ) ( )18, 0 , 0, 3−


1. always; The statement 2 2x y= implies that x and y

are the same number or opposites. In either case, x y= will always be true.

2. always; The Commutative Property of Addition is true for all real numbers.

3. sometimes; The equation has a solution if and only if 0.d ≥

8.2 Practice A

1.

vertical translation 4 units up; both open up; same axis of symmetry

2.


3.

vertical translation 2 units down; both open up; same axis of symmetry

4.

reflection in the x-axis; vertical translation 1 unit up; same axis of symmetry

5.

reflection in the x-axis; vertical translation 3 units down; same axis of symmetry

y

8

12

−2 2 x

y

8

4

12

−2 2 x

y

2

−3

−2 2 x

y

2

−2 2 x

−2

y

−2 2 x

−2

−6

Answers


A93

6.

vertical translation 2 units down; narrower; same axis of symmetry

7. vertical translation 3 units down; ( ) 22 2g x x= −

8. vertical translation 4 units up; ( ) 213

3g x x= +

9. 2x = ± 10. 8x = ±

11. 4x = ± 12. 5x = ±

13. a. 2 sec

b. 1 second later

14. Sample answer:

15.

16. Sample answer:

17. Sample answer:

18. yes; The vertex is ( )0, .c

8.2 Practice B

1.


y4

−2 2 x

y

4

2

6

−2 2 x

x

y

−2

2−2

3

y

8

4

−2 2 x

x

y

3−3

−2

−5

x

y

2−2

2

4

x

y

2−2

4

8

12

x

y

2−2

−2

−5

Answers


2.


3.

vertical translation 5 units down; both open up; same axis of symmetry

4.

reflection in the x-axis; narrower; vertical translation 4 units up; same axis of symmetry

5.

reflection in the x-axis; wider; vertical translation 1 unit down; same axis of symmetry

6.

vertical translation 5 units up; both open up; wider; same axis of symmetry

7. vertical translation 2 units down;

( ) 216

2g x x= − −

8. vertical translation 9 units down; ( ) 22 2g x x= −

9. 9x = ± 10. 5x = ±

11. 2x = ± 12. 3

2x = ±

13. 2.5x = sec to hit the ground; 100y = ft (height

of window)

14. a. Waterfall 1

b. Waterfall 3

c. They are the same, except Waterfall 2 drops water from a higher point.


1. odd 2. even

3. odd 4. neither

5. even 6. neither

3−3 x

y

−6

4

x

y

−4

6

3−3

x

y

−2

2

2−2

x

y

2

2−2

4

6

x

y

−8

−2 2

−12

x

y

4

−2 2

x

y

2−2

4

8

12

Answers


A95

7. neither 8. odd

9. even 10. neither

8.2 Puzzle Time

ON THE FRONT PERCH

8.3 Start Thinking

The coordinates of the y-intercept are ( )0, 1 . The

y-intercept of the equation can be determined by replacing x in the equation with zero.

( )( )

2

2

3 1

3 0 0 1

0 0 1

1

f x x x= − +

= − +

= + +=

( )( )

2

1

2 3

1

6

bx

a

−=

− −=

=

8.3 Warm Up

1. no 2. yes

3. no 4. yes


1. 3y ≥ −

2. 6t <

3. 46.5a >

4. 4t ≤ −

8.3 Practice A

1. vertex: ( )4, 2 ;− axis of symmetry: 4,x =

y-intercept: ( )0, 2

2. vertex: ( )2, 5 ;− − axis of symmetry: 2;x = −


3. a. 1x =

b. ( )1, 3−

4. a. 3

10x = −

b. 3 9

,10 20

− −

5. a. 1x =

b. ( )1, 8

6. a. 5

2x =

b. 5

, 402

7. x is all real numbers, 6y ≥ −

−9

−6

6

9

0−4 −2

−3

−6−8 2

5046

46.5

484442

x

y

2 4

−2

−4

−6

106 842

0−4 −2−6−8

Answers



9. x is all real numbers, 1y ≤


11. The value of a is 2− not 2.

( )16

42 2 2

bx

a= − = − =

−

12. minimum: 17−

13. maximum: 5

14. ( )1, 7 ;− The given point is 3 units right of the

vertex, so another point with the same y-coordinate is 3 units left of the vertex.

15. ( )6.12, 12.5− − 16. ( )0.34, 2.61

8.3 Practice B

1. vertex: ( )3, 4 ;− axis of symmetry: 3;x = −

y-intercept: ( )0, 2−

2. vertex: ( )1, 2 ;− axis of symmetry: 1;x = −


3. a. 3

2x = −

b. 3

, 92

− −

4. a. 2x = −

b. ( )2, 24−

5. a. 3

2x =

b. 3

, 312

6. a. 9

2x =

b. 9 3

,2 2

7. x is all real numbers, 7y ≥

8. x is all real numbers, 1y ≤ −


x

y

−10

−30

−2−6

x

y

−4

2−3

x

y

6

12

18

2 6

x

y

16

24

−2−4 2

x

y

−2 2

x

y

8 21

−10

−20

−30

Answers


A97


11. The incorrect y-coordinate of the vertex was found.

( )6

32 2 1

bx

a= − = − = −

( ) ( ) ( )23 3 6 3 2

7

f − = − + − +

= −

12. maximum: 19 13. minimum: 49−

14. ( )0.75, 4.18 15. ( )0.67, 2.43


1. 22,500 ft2 2. 5000 ft2

3. 4050 ft2 4. 2500 ft2

8.3 Puzzle Time

THE POST OFFICE

8.4 Start Thinking

( )( ) ( )

( )( ) ( )

2

2

2

3 1

3 1

3 1

f x x g x x

f x x g x x

x x

= = +

− = − − = − += − = +

The output values of the function ( )f x− are the

opposites of the output values of the function ( ).f x

The output values of the function ( )g x− are the

opposites of the output values of the function ( ).g x

8.4 Warm Up

1. ( )0, 0 2. ( )0, 2

3. ( )0, 0 4. ( )2.5, 6.25−

5. ( )0, 0 6. ( )0.16, 1.916−


1. nonlinear; The graph of the volume V as a function of s is quadratic because the formula for the solid’s volume is 28 .V s=

2. nonlinear; The graph of the volume V as a function of r is quadratic because the formula for the solid’s volume is 23 .V rπ=

3. linear; The graph of the volume V as a function of h is a line because the formula for the solid’s volume is 4 .V h=

4. linear; The graph of the volume V as a function of h is a line because the formula for the solid’s volume

is 256

.3

V hπ=

8.4 Practice A

1. neither 2. neither 3. even

4. even 5. neither

6. vertex; ( )2, 0 ;− axis of symmetry: 2x = −

7. vertex; ( )3, 0 ; axis of symmetry: 3x =

8. vertex; ( )7, 0 ;− axis of symmetry: 7x = −

9.

Both graphs open up. The graph of g is narrower than the graph of .f The graph of g is a translation

1 unit left and a vertical stretch by a factor of 2 of the graph of .f

x

y

4 62

4

8

x

y

2

4

6

2−2

Answers


10.


2 units right and a vertical stretch by a factor of 3 of the graph of .f

11.

Both graphs open up. The graph of g is wider than the graph of .f The graph of g is a translation

6 units left and a vertical shrink by a factor of 1

4 of

the graph of .f

12. vertex: ( )3, 2 ;− − axis of symmetry: 3x = −

13. vertex: ( )2, 5 ; axis of symmetry: 2x =


15.

Both graphs open up. The graph of g is a translation 3 units right and 2 units up of the graph of .f

16.

The graph of g is a reflection in the x-axis and a translation 2 units left and 4 units down of the graph of .f

17. ( )22 1 3y x= + −

18. ( ) ( )23 2 8f x x= − −

19. ( )24 3;y x= + − easy to find vertex and axis of

symmetry

2 8 13;y x x= + + easy to find the y-intercept

8.4 Practice B

1. neither 2. odd

3. even 4. odd

5. even

6. vertex: ( )6, 0 ;− axis of symmetry: 6x = −



9.


2 units left and a vertical stretch by a factor of 4 of the graph of .f

x

y

4

8

12

2 4

x

y

2

−2

−4−8−12

x

y

2

4

6

2 4 6

x

y

−4

−12

−2−4

x

y

−2−4

4

Answers


A99

10.

Both graphs open up. The graph of g is wider than the graph of .f The graph of g is a translation

5 units right and a vertical shrink by a factor of 1

3 of the graph of .f

11.

Both graphs open up. The graph of g is wider than the graph of .f The graph of g is a translation 1 unit

right and a vertical shrink by a factor of 1

6of the

graph of .f

12. vertex: ( )4, 3 ;− axis of symmetry: 4x =



15.

Both graphs open up. The graph of g is narrower than the graph of .f The graph of g is a vertical

stretch by a factor of 3 and a translation 2 units left and 1 unit down of the graph of .f

16.

The graph of g is wider than the graph of .f The

graph of g is a reflection in the x-axis, a vertical

shrink by a factor of 1

,2

and a translation 1 unit

right and 3 units up of the graph of .f

17. ( )25 1 3y x= − −

18. ( ) ( )22 2 13f x x= − − +

19. ( )23 2;y x= − − + easy to find vertex and axis of

symmetry

2 6 7;y x x= − + − easy to find the y-intercept


1.

2.

3.

x

y

2

2−2

−2

x

y

−4

4

x

y

−3 2

4

−2

x

y

−2−4 2

2

−2

x

y

2

−2

62

x

y

−2 2

4

−2

x

y

2

−2

4 62

Answers


4.

5.

6.

8.4 Puzzle Time

KNOW ALL THE ANGLES

8.5 Start Thinking

( )

( )( )

2

2

2 1

0 2 1

0 2 1 1

f x x x

x x

x x

= − −

= − −

= + −

2 1 0

1

2

x

x

+ =

= −

or 1 0

1

x

x

− ==

8.5 Warm Up

1. ( )( )2 7 2 7x x+ − 2. ( )( )4 2x x+ +

3. ( )( )2 1 5a a+ − 4. ( )3x x −

5. ( )( )4 1a a+ + 6. ( )( )2 1 4t t− +


1. 3 4y x= + 2. 2 2y x= − −

8.5 Practice A

1. The x-intercepts are 2− and 2 and the axis of

symmetry is 0.x =

2. The x-intercepts are 1− and 4− and the axis of

symmetry is 5

.2

x = −

3.

domain: all real numbers; range: 4y ≥ −

4.

domain: all real numbers; range: 9y ≤

5.


6.


x

y

2

−2

62

x

y

−2

−4

−2 2

x

y

2−2−4

x = −1

(−3, 0)

(−1, −4)

(1, 0)

xy

−20

−30

−10

62 (8, 0)(0, 0)

(4, −32)

x = 4

x

y

−8

2−10

(−7, 0)

x = −4

(−1, 0)

(−4, −9)

x

y

−2

−4

2

4

x

y

8

41

x = 2

(−1, 0) (5, 0)

(2, 9)

Answers


A101

7. 5 and 9 8. 3− and 2

9. 3− and 10 10. 2− and 5

2

11.

12.

13.

14.

15. Sample answer: ( ) 2 10 29f x x x= + +

16. Sample answer: ( ) 2 9 14f x x x= − +

17. Sample answer: ( ) 22 4 6f x x x= − − +

18. Sample answer: ( ) 2 6 9f x x x= + +

19. Sample answer: ( ) 2 16f x x= −

8.5 Practice B


symmetry is 5

.2

x = −


symmetry is 1.x = −

3.


4.


5.

domain: all real numbers; range: 0.25y ≥ −

6.


x

y

−4

2−2

x

y

8

4

−4

x

y

−4

−2

4 8 12

x

y

−6

−2

2−4

x

y

2

−4−1(−2.5, −1)

x = −2.5

(−3, 0)

(−2, 0)

x

y

−8

−12

−4

−10

x = −5

(−3, 0)

(−5, −8)

(−7, 0)

x

y

4

2

62

x = 3.5

(3.5, –0.25)

(3, 0) (4, 0)

x

y

10

2

(−2, 0) (4, 0)

x = 1

(1, 27)

Answers


7. 5 and 8− 8. 4− and 1

3−

9. 5, 5,− and 7− 10. 0, 9,− and 9

11.

12.

13.

14.


16. Sample answer: ( ) 2 3 40f x x x= + −

17. Sample answer: ( ) 214

2f x x x= + −


19. Sample answer: ( ) 2 6f x x= − +

20. a. 6 ft

b. 1.5 ft


1. Sample answer: To simplify is to write an expression in an easier form.

2. a. 4 3 25 7 35 ;x x x x− + + − degree 4; polynomial

b. 3 2 31 12 2 4

5;x x x+ − − degree 3; polynomial

c. 2 5;x− + degree 1; binomial

3. Sample answer: To factor is to break down an expression into parts.

4. a. degree 9; polynomial;

( )( )( )( )3 3 21 1 1 1x x x x x− + + − +

b. degree 2; binomial; ( )( )( )23 3 9x x x− + +

c. degree 2; trinomial; ( )( )3 2 6x x− + +

5. Sample answer: The roots of an equation are its solutions. The zeros of a function are where its graph crosses the x-axis.

6. a. 5, 4;x = − − The function has 2 zeros.

b. 3, 3;x = − The function has 2 zeros.

c. 5;x = The function has one zero.

7. The degree of each function and the number of zeros is the same, unless a zero has a multiplicity greater than 1.

8.

The function f has one zero, because it has one

x-intercept. The function g has two zeros, because it has two x-intercepts. The function h has no zeros, because it has no x-intercepts.

8.5 Puzzle Time

MEET YOU AT THE CORNER

x

y

2

−2

2 4 6

x

y

−20

−10

−4

x

y36

12

−2−4

x

y

−8

−4

3−3

x

y

4−4

−6

f

g

h

Answers


A103

8.6 Start Thinking

Sample answer:

linear exponential

quadratic

Linear Example: A company sells handkerchiefs for $4.50 each. The function ( ) 4.5f x x= models the

situation.

Exponential Example: The population of a city with 4000 people has decreased at an average rate of 4%

each year. The function ( ) ( ) ( )4000 0.96x

g x = models

the situation.

Quadratic Example: A ball is thrown straight up in the air from a height of 2 meters at a velocity of 15 meters per second. The function ( ) 25 15 2h x x x= − + +models the situation.

8.6 Warm Up

1. x-axis 2. Quadrant IV

3. Quadrant II 4. Quadrant I

5. Quadrant II 6. x-axis

7. Quadrant IV 8. Quadrant IV

9. Quadrant I 10. Quadrant IV

11. x-axis 12. Quadrant III


1. Sample answer: 2 4

4 15 44

x y

x y

− + = −− + =


7 11 122

x y

x y

− + = −− + = −


9 6 33

x y

x y

− + =+ =


3 10 308

x y

x y

− + = −− =


2 7

x y

x y

− + =+ =


8 26

x y

x y

− + =− = −

8.6 Practice A

1. exponential 2. linear

3.

quadratic

4.

linear

Type of function

General form Graph characteristics

linear y mx b= + straight line

exponential xy ab= curved graph, steep increase or decrease

quadratic 2y ax

bx c

= ++

U-shaped graph

x

y

2

−2

−2

2

x

y

4

6

2

2−2

x

y

2

−2

2−2

x

y

4

2

2−2

x

y

4

2

4−4

Answers


5.

quadratic

6.

exponential

7. a. March

b.

quadratic

c. 2 6 10y x x= − +

d. 26,000

8.6 Practice B

1. quadratic 2. exponential

3.

exponential

4.

quadratic

5.

linear

6.

linear

7. quadratic 8. linear

9. quadratic 10. exponential

11. Sample answer: 22 2 4y x x= − +


1. decreasing: ( ), 2 ;−∞ increasing: ( )2, ∞

2. decreasing: ( )3, 1 ;− increasing: ( ) ( ), 3 1,−∞ − ∪ ∞

3. decreasing: ( ) ( ), 2 0, 2 ;−∞ − ∪ increasing:

( ) ( )2, 0 2,− ∪ ∞

4. decreasing: ( )1, 1 ;− increasing: ( ) ( ), 1 1, −∞ − ∪ ∞

8.6 Puzzle Time

TO A SHED

x

y

8

4

2−2

x

y

8

10

4

2 4 6

x

y

8

4

2−2

x

y

2

−2

−2

2

x

y

2

−4

−2

4

x

y

2

−2

−2

2

x

y4

−8

−4

2−2

Answers


A105

Cumulative Review

1. all real numbers 2. 4, 8y = −

3. all real numbers 4. no solution

5. 7x < − or 2x > −

6. $15.50 or more 7. 32 38x + ≤

8.

9.

10. 5y x= + 11. 2

53

y x= −

12. 2 2y x= + 13. ( )1, 2− −

14. ( )1, 3− 15. ( )7, 2−

16. $4 children, and $7 adult

17. 2

7

2

3

x

yz 18.

7

3

m

19. 73x

yz 20. 4

21. 16 22. 3−

23. 1

4y = 24. 7y = −

25. 1

28y =

26. ( )1000 1 0.05 ,t

y = + where yearst =

27. ( )60 1 0.80 ,t

y = − where yearst =

28. 17x = 29. 5x =

30. 12x = 31. 2 4g +

32. 8 2h− + 33. 4 15x− −

34. 16 14y + 35. 2 2 24x x− −

36. 2 3 40y y− − 37. 2 4 4x x+ +

38. 29 30 25m m− +

39. 2 2121 110 25x xy y+ +

40. 4, 3x = − 41. 0, 8g =

42. ( )( )15 1m m+ − 43. ( )( )8 3z z+ −

44. ( )( )17 1x x− + 45. ( )( )5 2 4x x− −

46. ( )( )2 1 2y y− + 47. ( )( )4 1 2w w+ −

48. 0.75 sec 49. ( )( )11 11x x+ −

50. ( )( )12 12a a− − 51. ( )( )4 3 3b b+ −

52. 9, 9z = − 53. 13y =

54. ( )( )22 3 4x x− + 55. ( )( )25 7 2y y+ −

56.

vertical stretch by a factor of 4

57.

vertical shrink by a factor of 0.2

x

y

2

−2

x

y

−4

−6

−2

2−2

x

y

−8

−12

2−2

x

y

2

−2

−2

2

Answers


58.

vertical shrink by a factor of 2

5 with a reflection in

the x-axis

59.

vertical stretch by a factor of 7 with a reflection in the x-axis

60.

vertical shrink by a factor of 0.625 with a reflection in the x-axis

61.

vertical shrink by a factor of 1

2

62.

translation 3 units up

63.

translation 10 units up

64.

translation 10 units down

65.

a reflection in the x-axis and a translation 2 units down

66.

vertical stretch by a factor of 4 and a translation 2 units up

x

y

−2

−16

−24

2

x

y

2

−2

−2

2

x

y

2

−2

−2

2

x

y

2

4

6

−2 2

x

y

6

12

18

−2 2

x

y

−2 2

−8

−4

x

y

−2 2

−4

−6

x

y

−2 2

8

12

x

y

2

−2

−2

2

Answers


A107

67.

reflection in the x-axis, a vertical shrink by a factor

of 1

,5

and a translation 5 units down

68. 2, 2− 69. 2, 2− 70. 3 3

,5 5

−

71. a. 2.5 sec

b. If k is positive it will increase the answer for part (a), and if k is negative it will decrease the answer for part (a).

72. axis of symmetry: 2;x = − vertex: ( )2, 31−

73. axis of symmetry: 3;x = vertex: ( )3, 66

74.


75.




80. odd 81. even 82. neither




86. vertex: ( )7, 8 ;− axis of symmetry: 7x =


88.

translation 3 units right and a vertical stretch by a factor of 2

89.

translation 1 unit to the left and 5 units up, and a vertical stretch by a factor of 4

90.

91.

x

y

−4−10

7

42

x

y

6 12

90

30

60

x

y

2 4

4

2

x

y

2−2

10

4

x

y

10

−10

42

x

y54

9

84−4

x

y

−4

−6

−2

2−2

Answers


92.

93.

94. 7,1x = − 95. 13, 2x = − −

96. 3, 3x = − 97. 2, 5x = −

98. linear function: 3 10y x= +

99. quadratic function: 2 9y x= −

100. exponential function: 3xy =

Chapter 9 9.1 Start Thinking

360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Greatest perfect square: 36

360 36 10

36 10

6 10

= •

= •

=

9.1 Warm Up

1. 4 2. 8 3. 15

4. 45 5. 240 6. 6

7. 20 8. 2 9. 60


1. exponential decay; 30%

2. exponential growth; 4%



9.1 Practice A

1. 5 2 2. 2 17 3. 7 2−

4. 3

5 5.

3

8− 6.

2

x−

7. 32 3 8. 35 2− 9. 34 2x x−

10. found square root instead of cube root

3 3

33

3

16 8 2

8 2

2 2

= •

= •

=

11. 5

5 12.

7

7

n

n 13.

3

3

3

3

14. 3 15. 9 5

5 16.

6

10

17. 4 w

w 18.

5

5

t

t 19.

14

7

z

20. 6 1

5

+ 21.

12 3 2

14

− 22.

5 3 6

23

+

23. 0.027

9.1 Practice B

1. 3 6 2. 5y 3. 3 2n n−

4. 29

10 5.

7

p p 6. 2

x

7. 232 4q 8. 3 9

2

d− 9. 3 260

9

x

y−

10. not fully simplified; the denominator contains a radical

30 30 30

25 525= =

11. 7

7

y

y 12.

3

3

k

k 13.

3 6

3 6

++

14. 4 3

3 15.

10

15 16.

6

6

t

t

x

y

4 8−4

10

x

y

4−4

−24

−12

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