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
Answers
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers
A109
17. 35
7
h 18.
2
3 6
2
d
d 19.
325 2
2
20. 35 5 2
47
+ 21.
8 3 21
57
−
22. 5 35
2
− − 23.
3 323 3 3
1
x x
x
+ +−
9.1 Enrichment and Extension
1. 4 5i 2. 5 2iy x 3. 6 6i
4. 24 2iwz 5. 35 7ir pq 6. 22ix x
7. 5i 8. 2 3i 9. 10
5
i
10. 2 10i 11. 9i 12. 2 15ixy x
13. 3 10
4
i− 14. 3 2
2
i
− 15.
2iy
x
−
9.1 Puzzle Time
THANK YOU FERRY MUCH
9.2 Start Thinking
The parabola crosses the x-axis twice. The points are
( )1, 0− and ( )3, 0 .
The zeros of the function show the same points because a “zero” is another name for a point where the parabola crosses the x-axis. These points are called zeros because they represent the point(s) on the parabola where the y-value is zero.
9.2 Warm Up
1. 2x = − 2. 2b = 3. 4x =
4. 5y = − 5. 0y = 6. 1n =
9.2 Cumulative Review Warm Up
1. 0 or 9x x= = 2. 0 or 2t t= = −
3. 0 or 10s s= = − 4. 2 or 4a a= − =
5. 1
2m = 6. 4 or 4g g= − =
9.2 Practice A
1. 1, 4x = − 2. 2, 5x =
3. 23 15 0x − = 4. 2 14 0x− + =
5. 22 4 5 0x x− + − = 6. 0, 3x = −
7. 1x = − 8. no solution
9. 5, 1x = − 10. no solution
11. 1, 3x = −
12. a. They indicate when the height is zero.
b. 4 ft
13. 6, 2x = − 14. 3, 5x = 15. 1, 10x = −
16.
0.4, 2.6x =
17.
0.8, 7.2x =
18.
7.6,1.6x = −
−5
5
−5
5
4
4
x
y
f(x) = x2 − 3x + 1
42 6
4
0
8
x
y
f(x) = −x2 + 8x − 6
x
y
−2−4
y = 13 x2 + 2x − 4
Answers
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A110
19.
no solution
20. 3 ftx =
9.2 Practice B
1. 3x = − 2. no solution
3. 2 23 0x− − = 4. 25 9 3 0x x− − + =
5. 27 2 6 0x x− − + = 6. 0, 6x =
7. 6x = 8. no solution
9. 1, 7x = − 10. no solution 11. 9, 1x = −
12. a. no; Time cannot be negative.
b. 2 sec
13. 7, 1x = − 14. 5, 4x = − − 15. 12, 2x = −
16.
4.6, 0.4x = − −
17.
1, 3x =
18.
no solution
19.
0.4, 5.6x =
20. 6 ft
9.2 Enrichment and Extension
1. a. 2.25 sec and 4 sec b. 6.25 sec
2. 60 ft 3. 8.5 years; in 1998
4. a. 1000 tires b. $35
9.2 Puzzle Time
IT HAS NO STEPS
x
y
−2
−2 2
y = −2x2 + 3x − 2
x
y
−4
−2
f(x) = x2 + 5x + 2
42
2
x
y
f(x) = x2 − 4x + 3
x
y
−2
2 4 6
y = 12 x2 − 3x + 1
x
y
−4
−2
2 4
y = −x2 + 3x − 5
Answers
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers
A111
9.3 Start Thinking
Replacing ( )f x with zero and moving the constant
yields the following equations:
2 4x = 2 9x = 2 0x = 2 0x = 2 4x = −
2 9x = −
When the constant is positive, there are two solutions; when the constant is zero, there is one solution; and when the constant is negative, there are no solutions.
9.3 Warm Up
1. 5x = 2. 6x =
3. 2w = − 4. 2a = −
9.3 Cumulative Review Warm Up
1. even 2. neither
3. neither 4. odd
9.3 Practice A
1. two; 6, 6x = − 2. zero
3. one; 0x = 4. 3, 3x = − 5. no solution
6. no solution 7. 8, 8x = − 8. 6, 6x = −
9. 0x = 10. 4x = 11. 5,1x = −
12. 8
, 23
x = − 13. 2.45x = ± 14. 4.24x = ±
15. 2.24x = ±
16. The square root does not distribute over subtraction,
so 2 9x − does not equal 3.x − Begin by
isolating 2x on the left side.
2
2
9 16
25
5
x
x
x
− =
== ±
17. a. 221 336w =
b. width 4 cm, length 12 cm
18. At 5,x = ± because 2 25.x =
19. At 1.1,x = ± because 2 1.21.x =
9.3 Practice B
1. two; 11,11x = − 2. zero
3. two; 14,14x = − 4. no solution
5. 2, 2x = − 6. 0x = 7. 3, 3x = −
8. 1 1,
3 3x = − 9.
9 9,
2 2x = − 10. 12, 2x = −
11. 1
, 22
x = − 12. 2 12
,5 5
x = −
13. 2.65x = ± 14. 2.83x = ± 15. 1.11x = ±
16. The right side becomes negative after subtracting 25, so the equation does not have a real solution.
2
2
25 9
16
x
x
+ =
= −
no solution
17. a. 210 160rπ π= b. 4 in.
18. a. 8, 2x = −
b. 12, 2x = −
c. 5, 5x = −
9.3 Enrichment and Extension
1. 0;x = multiplicity of 2; rational
2. ;x i= ± imaginary
3. 5 ;x i= ± imaginary
Function Number of zeroes
( ) 2 4f x x= − 2
( ) 2 9f x x= − 2
( ) 2f x x= 1
( ) 2f x x= − 1
( ) 2 4f x x= + 0
( ) 2 9f x x= + 0
Answers
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A112
4. 2 3;x = ± irrational
5. 6
;2
x = ± irrational
6. 2 3
;3
ix = ± imaginary
7. 2 ;x i= ± imaginary
8. 10
;2
ix = ± imaginary
9. 2 2 ;x i= ± imaginary
9.3 Puzzle Time
HOW ABOUT SECONDS
9.4 Start Thinking
The minimum and the vertex are the same point for the function.
A quadratic function has a minimum when the parabola opens up and a maximum when the parabola opens down; these correspond to positive and negative leading coefficients, respectively.
9.4 Warm Up
1. ( )( )3 3x x+ − 2. ( )21y +
3. ( )( )2 1 2 1x x+ − 4. ( )24x −
5. ( )22 1a + 6. ( )( )1 7 1 7x x+ −
7. ( )23 1a + 8. ( )2
2 5a −
9.4 Cumulative Review Warm Up
1. 11z = 2. 4m = − 3. 2c =
4. 3y = − 5. 3g = − 6. 2h = −
7. 30n = 8. 19n = −
9.4 Practice A
1. 9c = 2. 25c = 3. 1c =
4. ( )22 4 4 2x x x− + = −
5. ( )22 20 100 10x x x− + = −
6. ( )22 26 169 13x x x+ + = +
7. 0.69, 8.69x = − 8. 1,11x =
9. 18.38, 0.38x = −
10. a. 2 12 160w w+ =
b. width 8 ft, length 20 ft
11. no solution 12. 5, 3x = −
13. 1.55, 6.45x = 14. 1, 7x = − −
15. 5.61,1.61x = − 16. 0.55, 5.45x =
17. Divide every term by 5.
18. minimum of 13− 19. minimum of 6−
20. maximum of 29 21. minimum of 40−
22. a. 2 2 224x x+ = b. 14− and 16−
9.4 Practice B
1. 64c = 2. 1
4c = 3.
49
4c =
4. ( )22 14 49 7x x x− + = −
5. ( )22 30 225 15x x x+ + = +
6. 2
2 81 99
4 2x x x
− + = −
7. 11.4,1.4x = − 8. 1.54, 4.54x = −
9. 15.76, 0.76x = −
10. a. 2 12 108− =
b. width 6 ft, length 18 ft
4 x
y
−2
2
(–2, –5)
x
y
−4
4
(1, –2)
Answers
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers
A113
11. 2.17, 7.83x = 12. 20.8, 1.2x = − −
13. no solution 14. 19.17, 0.83x = − −
15. 5.61,1.61x = − 16. 1.37, 4.37x = −
17. 14b = ± 18. minimum at 5−
19. minimum at 39− 20. maximum at 9
4−
21. minimum at 5
22. a. 2 2 323x x+ =
b. 17 and 19
9.4 Enrichment and Extension
1. ( ) ( )21 5; 1, 5y x V= − +
2. ( ) ( )23 8; 3, 8y x V= + − − −
3. ( ) ( )21 4; 1, 4y x V= − + − − −
4. ( ) ( )23 1 1, 1, 1y x V= − − −
5. ( ) ( )22 3 3; 3, 3y x V= − +
6. ( ) ( )23 2 5; 2, 5y x V= − + − − −
7. ( ) ( )25 1 5; 1, 5y x V= + − − −
8. ( ) ( )214 1; 4, 1
2y x V= − − +
x2
y
4
x
y
2
−6
−4 −2
x2
y
−6
−2
−2
x
y
2
2
x
y
4
8
2 4
x
y
−4
−4 −2
x
y
−1
4
x
y
−4
4 8
Answers
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A114
9. ( ) ( )223 6; 3, 6
3y x V= + − − −
9.4 Puzzle Time
A HARE RESTORER
9.5 Start Thinking
When 0,a = the Quadratic Formula is undefined because you cannot divide by zero. In this case, the function has no 2x term, and is therefore not quadratic but linear.
The other situation that makes the Quadratic Formula undefined is when 2 4 0.b ac− < Note: In this case, the equation is technically still solvable, using the set of imaginary numbers.
9.5 Warm Up
1. 23 2. 361− 3. 477
4. 191 5. 39− 6. 0.699
9.5 Cumulative Review Warm Up
1. 2 or 7w w≤ ≥
2. 5 1
3 3u− < < −
3. 4 0f− < <
4. 1 9
or5 5
v v≤ ≥
5. 7 17x− < <
6. no solution
9.5 Practice A
1. 2 5 0;x x+ = 1,a = 5,b = 0c =
2. 2 3 10 0;x x+ + = 1,a = 3,b = 10c =
3. 25 7 2 0;x x− − + = 5,a = − 7,b = − 2c =
4. 3x = − 5. no real solution
6. 1, 10x = − 7. 1
1,3
x = −
8. no real solution 9. 1
2x = −
10. 2 3
,3 2
x = − 11. 0.3, 2.1x = −
12. a. 0.3 and 0.8 sec b. 1.125 sec
13. one 14. two 15. zero
16. two 17. zero 18. two
19. 2;x = ± Using Square Roots; in the form 2x d=
20. no real solutions; Quadratic Formula; doesn’t fit the other methods
21. 0.4, 8.4;x = − completing the square; 1a = and
b is even.
22. 3.4, 2.4;x = − Quadratic Formula; doesn’t fit the
other methods
23. 7;x = factoring; Perfect Square Trinomial
24. 0, 5;x = factoring; easy to factor
25. a. 47 0;− < no real solutions
b. 23 5 6 0x x− + =
c. no; Both equations have zero solutions; the sign of b does not affect the discriminant because b is squared.
9.5 Practice B
1. 2 2 9 0;x x+ − = 1,a = 2,b = 9c = −
x
y
4
−6
−8 −4
0 3 6
2 7
9−3 12
0−2 −1 143
−53
− 23
− 23
13
− 13
0−2 642−6 −4
0−2 542 31−5 −4 −1−3
95
15
0 4 8
−7 17
12 16−4 20−8
Answers
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers
A115
2. 27 6 1 0;x x− + − = 7,a = − 6,b = 1c = −
3. 24 10 7 0;x x− − = 4,a = 10,b = − 7c = −
4. 4x = 5. 1, 11x = −
6. 1
, 32
x = 7. 0.2, 0.8x = −
8. no real solution 9. 1x = −
10. 0.3, 1.4x = − 11. no real solution
12. a. 6.5 and 13.5 sec b. 21.2 sec
13. zero 14. two 15. one
16. one 17. zero 18. two
19. 20.6,x = 0.6;− completing the square; 1a =
and b is even.
20. 0,x = 3;− factoring; easy to factor
21. no real solution; using square roots; in the form 2x d=
22. 0.1,x = 1.4;− Quadratic Formula; doesn’t fit the
other methods
23. 1.1,x = − 1.9; Quadratic Formula; doesn’t fit the
other methods
24. 6;x = factoring; Perfect Square Trinomial
25. a. 47 0− < b. 23 5 6 0x x+ − =
c. yes; The original equation has zero solutions and the new equation has two solutions; changing the sign of c changes the discriminant from negative ( )47− to positive ( )97 .
9.5 Enrichment and Extension
1. 9 in.
2. length: 9 km, width: 12 km
3. width: 12 in., height: 16 in.
4. base: 22 4.7 in.,≈ height: 3 22 14.1 in.≈
5. height: 8 10 25.3 cm, base: 10 10 31.6 cm≈ ≈
9.5 Puzzle Time
THEIR TRUNKS
9.6 Start Thinking
System 1 has two solutions because the graphs of the equations intersect at two points.
System 2 has one solution because the graphs of the equations intersect at one point.
System 3 has no solution because the graphs of the equations do not intersect.
9.6 Warm Up
1. ( )1, 3− 2. ( )1, 3− −
3. ( )1, 1− 4. ( )2, 3
9.6 Cumulative Review Warm Up
1.
x-intercept: ( )5, 0
5
−12
−5
12
= 2-10y x
=8y
6
−2
−4
8
= +44y x = 2+4 +4-y x x
5
−2
−5
6
= 2-3-4y x x
=6+2y x
2 6
−4
−2
x
y
Answers
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A116
2.
x-intercept: ( )0, 0
3.
x-intercept: ( )1, 0−
4.
x-intercept: 1
, 03
−
9.6 Practice A
1. ( ) ( )1, 2 , 0, 1− − 2. no real solution
3. ( )1, 3 4. ( ) ( )2, 1 , 4, 3− −
5. ( ) ( )0, 4 , 4, 0− 6. ( )2, 8
7. ( ) ( )7, 23 , 1, 5 8. ( ) ( )2, 1 , 5, 22− − −
9. ( ) ( )2, 1 , 1,2− − 10. ( ) ( )1, 4 , 3, 20− −
11. no real solution 12. ( ) ( )2, 4 , 2, 0−
13. a zero between 3− and 2− ; a zero between 1−
and 0
14. a zero between 1 and 3; a zero between 3 and 4
15. at 1.7t = sec
9.6 Practice B
1. ( ) ( )1, 5 , 2, 11− 2. ( ) ( )3, 10 , 0, 5−
3. ( )1, 4− 4. no real solution
5. ( )3, 18 6. no real solution
7. ( ) ( )7, 31 , 2, 4− − − 8. ( )0, 3−
9. ( )1, 1− 10. ( ) ( )3, 12 , 1, 4−
11. ( ) ( )1, 12 , 4, 7− 12. ( ) ( )3, 8 , 1, 0− −
13. a zero between 0 and 1
14. a zero between 0 and 1; a zero between 1 and 2
15. Sample answer: ( ) 21.6 2 5.6;f x x x= + −
( ) 22.5 2 4.2;g x x x= − − − corresponding
solutions are ( ) ( )1.25, 5.6 , 0.27, 4.93 .− − −
9.6 Enrichment and Extension
1. a. at 1t = sec, and then again at 3t = sec
b. 4.09 sec
2. 80, or 40 jackets 3. 435 items
4. a. yes
b. about 0.52 and 0.26 sec
5. a. about 0.59 sec
b. 1.07 sec
9.6 Puzzle Time
TO BE ABOVE IT ALL
Cumulative Review
1. 4x = −
2. 3, 4y y= − =
3. 5 4h− ≤ ≤
2 4
2
4
−4
−4 −2
x
y
2 4
2
4
−4
−2
−4
x
y
2 4
2
4
−4
−4 −2
x
y
0 4
−5
8−4−8
Answers
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers
A117
4. 2y ≤
5. no solution
6. a. 350 1050y x≥ +
b. at least 4 h
7. 2 4 14x − ≥
8.
9.
10.
11. 1
32
y x= − + 12. 4 12y x= −
13. 1
162
y x= − − 14. ( )3, 2−
15. ( )6, 4− 16. no solution
17. $7 for a small box and $13 for a large box
18. 9
1
4x yz 19. 37m
20. yz
x 21. 1x =
22. 9x = 23. 10x = −
24. 4 13g− + 25. 3 2y −
26. 2 5 24x x+ − 27. 2 249 42 9x xy y+ +
28. 4, 6x = − 29. 0, 5g =
30. ( )( )4 2m m− − 31. ( )( )5 7z z+ −
32. ( )( )2 2 1w w+ + 33. 1 sec
34. 5, 5z z= − = 35. 11y = −
36. ( )( )23 4 5x x− − 37. ( )( )24 7 1y y− −
38.
vertical stretch by a factor of 5
39.
vertical shrink by a factor of 0.375
40.
vertical shrink by a factor of 3
7and a reflection in
the x-axis
0 6
2
12−6−12
1
2
−2 x
y
−1
4
2
x
y
−2
2−2 x
y
−2
2
2
−2 x
y
−2
2
2
−2 x
y
−2
4−4 x
y
−4
4
Answers
Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A118
41.
translation 6 units up
42.
vertical stretch by a factor of 3, followed by a translation 7 units up
43.
vertical shrink by a factor of 1
,8
and a reflection in
the x-axis, followed by a translation 3 units down
44. a. 25 sec
b. If k is positive, it will increase part (a); if k is negative, it will decrease part (a).
45. a. axis of symmetry : 3x = −
b. vertex: ( )3, 30−
46. a. axis of symmetry: 5x =
b. vertex: ( )5, 80−
47.
domain : all real numbers; range: 1y ≥ −
48.
domain: all real numbers; range: 15y ≤
49. maximum: 4 50. minimum: 91−
51. vertex: ( )3, 0 ; axis of symmetry: 3x =
52. vertex: ( )5, 0 ;− axis of symmetry: 5x = −
53. vertex: ( )5, 4 ; axis of symmetry: 5x =
54.
translation 6 units to the left and a vertical stretch by a factor of 7
55.
translation 2 units to the right and 8 units down,
followed by a vertical shrink by a factor of 4
7
56.
2
4
8
12
−2 x
y
2
2
6
12
−2 x
y
4−4 x
y
−4
−2
2
2
−2 x
y
−2
2
16
8
−2 x
y
4
2
−8 −4 x
y
2 4
xy
−8
−2
x
y
−20
−30
−10
84−4−8
Answers
Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers
A119
57.
58. quadratic function; 2 4 12y x x= + −
59. 4 5y y 60. 2
3
61. 3 2 2 6− − 62. 3 2
3
2 4
5
x x
y
63. 5 30 3 2− + 64. 1
2
65. 9, 4x x= − = 66. 1, 1x x= − =
67. 5, 1x x= − = 68. 3, 4x x= =
69. 4x = ± 70. 5x = ±
71. no real solutions 72. 2 sec
73. 2, 1x x= − = − 74. 2, 10y y= − = −
75. 17.3, 1.3w w≈ − ≈ 76. 7, 3t t= − = −
77. 2, 4n n= − = 78. 8
4,3
h h= − = −
79. a square fence, with side length 15 ft
80. 3 1
,2 2
x x= − = − 81. 5
4,2
y y= − =
82. 0.4, 3.9w w= − = 83. 1.8, 1.3z z= − =
84. 0 x-intercepts 85. 1 x-intercept
86. 2 x-intercepts 87. 0 x-intercepts
88. ( )2, 2− and ( )4, 10− 89. ( )2, 4− − and ( )1, 1−
90. no solution 91. 3 in. by 12 in.
Chapter 10 10.1 Start Thinking
The domain of the function is all positive real numbers and zero. The range is also all positive real numbers and zero. You cannot use negative numbers in the domain because the square root function cannot be evaluated using negative numbers in this course.
The calculator is able to graph this function because negative numbers and zero will allow the radical to be evaluated. This function has an inverse domain when compared to .y x=
10.1 Warm Up
1.
2.
x
y4
−12
84−4−8
5
−5
−5
5
5
−5
−5
5
−2
−4
2 4 x
y
−2−4
3
−2
−4
2 4 x
y
−2−4
4
2
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