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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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A90
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.
vertical stretch by factor of 7
;2
both open up; same
vertex; same axis of symmetry
4.
vertical stretch by factor of 5
;3
reflection in the
x-axis; same vertex; same axis of symmetry
5.
vertical shrink by factor of 3
;4
reflection in the
x-axis; same vertex; same axis of symmetry
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A92
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−
8.2 Cumulative Review Warm Up
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.
vertical translation 7 units up; both open up; same axis of symmetry
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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.
vertical translation 5 units up; both open up; same axis of symmetry
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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A94
2.
vertical translation 10 units up; both open up; same axis of symmetry
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.
8.2 Enrichment and Extension
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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
8.3 Cumulative Review Warm Up
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 = −
y-intercept: ( )0, 3
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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A96
8. x is all real numbers, 29y ≥ −
9. x is all real numbers, 1y ≤
10. x is all real numbers, 20y ≤
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 = −
y-intercept: ( )0, 5
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 ≤ −
9. x is all real numbers, 29y ≥ −
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers
A97
10. x is all real numbers, 8y ≤
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
8.3 Enrichment and Extension
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−
8.4 Cumulative Review Warm Up
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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A98
10.
Both graphs open up. The graph of g is narrower than the graph of .f The graph of g is a translation
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 =
14. vertex: ( )5, 4 ;− − axis of symmetry: 5x = −
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 = −
7. vertex: ( )4, 0 ; axis of symmetry: 4x =
8. vertex: ( )9, 0 ;− axis of symmetry: 9x = −
9.
Both graphs open up. The graph of g is narrower than the graph of .f The graph of g is a translation
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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 =
13. vertex: ( )1, 5 ;− axis of symmetry: 1x = −
14. vertex: ( )3, 2 ;− − axis of symmetry: 3x = −
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
8.4 Enrichment and Extension
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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A100
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− +
8.5 Cumulative Review Warm Up
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.
domain: all real numbers; range: 32y ≥ −
6.
domain: all real numbers; range: 9y ≥ −
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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
1. The x-intercepts are 5− and 0 and the axis of
symmetry is 5
.2
x = −
2. The x-intercepts are 6− and 4 and the axis of
symmetry is 1.x = −
3.
domain: all real numbers; range: 1y ≥ −
4.
domain: all real numbers; range: 27y ≤
5.
domain: all real numbers; range: 0.25y ≥ −
6.
domain: all real numbers; range: 8y ≥ −
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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A102
7. 5 and 8− 8. 4− and 1
3−
9. 5, 5,− and 7− 10. 0, 9,− and 9
11.
12.
13.
14.
15. Sample answer: ( ) 2 12 34f x x x= − +
16. Sample answer: ( ) 2 3 40f x x x= + −
17. Sample answer: ( ) 214
2f x x x= + −
18. Sample answer: ( ) 2 2 1f x x x= − +
19. Sample answer: ( ) 2 6f x x= − +
20. a. 6 ft
b. 1.5 ft
8.5 Enrichment and Extension
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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
8.6 Cumulative Review Warm Up
1. Sample answer: 2 4
4 15 44
x y
x y
− + = −− + =
2. Sample answer: 2 7
7 11 122
x y
x y
− + = −− + = −
3. Sample answer: 2 9
9 6 33
x y
x y
− + =+ =
4. Sample answer: 2 58
3 10 308
x y
x y
− + = −− =
5. Sample answer: 2 1
2 7
x y
x y
− + =+ =
6. Sample answer: 2 8
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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A104
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= − +
8.6 Enrichment and Extension
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A106
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
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. 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.
domain: all real numbers; range: 41y ≤
75.
domain: all real numbers; range: 80y ≤
76. maximum: 53 77. minimum: 94−
78. maximum: 18 79. minimum: 15−
80. odd 81. even 82. neither
83. vertex: ( )2, 0 ; axis of symmetry: 2x =
84. vertex: ( )1, 0 ; axis of symmetry: 1x =
85. vertex: ( )3, 0 ;− axis of symmetry: 3x = −
86. vertex: ( )7, 8 ;− axis of symmetry: 7x =
87. vertex: ( )2, 9 ;− axis of symmetry: 2x = −
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
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A108
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
9.1 Cumulative Review Warm Up
1. exponential decay; 30%
2. exponential growth; 4%
3. exponential decay; 5%
4. exponential decay; 20%
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