CHAPTER 5
Think & Discuss (p. 247)
5.1 Guided Practice (p. 253)
1. parabola
1. about 1900 ft
2. Up; since a 3 and is greater than 0, the
parabola opens up.
2. about 22 sec; Sample answer: The graph charts the lava
fragment in the air from its initial point at zero until there
are no longer fragments in the air at 22 sec.
3. intercept form
4.
5.
y
Skill Review (p. 248)
x
4.
3. 2x 1 x 7
4x 12
3x 6
x 3
x2
5
3
5.
y
1 x
(2, 3)
y 2(x 1)2 4
1
x
1
x2
6.
x 1
x 0.5
y
(0.5, 2.25)
1
x
1
1
y (x 2)(x 1)
3x 2y 12
1
1
1 x
6.
7.
y
y
y 2x
1
1
x
1
7.
y x 2
(0, 2)
1
1
1
9.
y
y
3
1
1
y 3 x 2 2x 3 (3, 0)
x
1
1
1
y x 3
1
1
x 3
x
8.
y
(4, 6)
3
y 5 (x 4)2 6
(1, 4)
1
1 x
y
1
1
1
(1, 4)
x
1
1
y
1
1
y5x
8.
1
y x 2 4x 7
1. 3x 5 0 2. 4x 24 12
3x 5
y
(3, 0) x
y 2x 1 4
1
Lesson 5.1
x
1
1
x4
Activity (p. 29)
9.
1.
2.
y
1
1
1
x
1
5
y 2 x(x 3)
(1.5, 5.625)
3. 0, 0; x 0
4. The graph opens up if a > 0, the graph
x 1.5
opens down if a < 0.
124
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
10. y x 1x 2
11. y 2x 4x 3
24.
x 4
y
y 2x2 x 12
y x2 3x 2
y 2x2 2x 24
12. y 4x 12 5
y 4x2 2x 1 5
y x2 4x 4 7
y 4x2 8x 9
y x2 4x 11
12x 6x 8
12x2 14x 48
12x2 7x 24
2
2
3 x 9 4
2 2
3 x 18x 81 2 2
3 x 12x 50
14. y y
y
15. y y
y
16. males: x 1
13. y x 22 7
x
1
1
1
y 2 x 2 4x 5
25.
x 3
18. A
20.
y
1
(3, 1.5)
y
1
6 x 2
1
1
x3
1 x
4
612.6
908.9
71.4F; females: x 73F
8.58
12.448
26.
27.
y
x2
y
1
y (x 1)2 2
5.1 Practice and Applications (pp. 253–255)
17. C
(4, 3)
1
1
y x1
(2, 1)
1
x
y (x 2)2 1
(1, 2)
1
19. B
1
x
x1
28.
x 3
y
1
y x 2 2x 1
x
1
1
1
1
1
y 2(x 3)2 4 (3, 4)
x
(1, 2)
21.
y
29.
y
y 2x 2 12x 19
1
x3
x 4
1
1
x2
y
(2, 2)
y x 2 4x 2
1
1
(4, 5)
x
1
1
22.
y 3(x 4)2 5
(3, 1)
30.
y
(1, 3)
1
y 3 (x 1)2 3
x
1
x
1
1
23.
x
x 1
y
31.
x0
y
(0, 5)
y 3x 2 5
5
y 4 (x 3)2
1
1
1
1
x
Copyright © McDougal Littell Inc.
All rights reserved.
1
1
(3, 0)
x
x3
Algebra 2
Chapter 5 Worked-out Solution Key
125
Chapter 5 continued
32.
41. y 3x 7x 4
y
x4
1
y 3x2 7x 4x 28
(2, 0)
y 3x2 9x 84
x
(6, 0)
1
42. y 5x 84x 1
y (x 2)(x 6)
(4, 4)
33.
y 20x2 37x 8
y x2 6x 11
y x2 10x 25 11
(1, 0)
y x2 10x 14
x
2
45. y 6x 2 9
y 4(x 1)(x 1)
y 6x2 4x 4 9
x0
y 6x2 24x 33
34.
x 4
y (x 3)(x 5) (4, 1)
9
y x2 6x 9 2
44. y x 5 11
(1, 0)
(0, 4)
y 20x2 32x 5x 8
2
y
1
43. y x 32 2
y 8x2 14x 49 20
1
(3, 0)
(5, 0)
46. y 8x 72 20
y
y 8x2 112x 372
x
1
47. y 9x 22 4x
y 81x2 36x 4 4x
y 81x2 32x 4
35.
x 2.5
48. y 3 x 6x 3
7
y
y 73x2 9x 18
y 73x2 21x 42
(1, 0)
49. y 2 8x 12 1
(4, 0)
y
1
(x
3
4)(x 1)
1 x
1
y 1264x2 16x 1 32
(2.5, 0.75)
36.
y
3
2
y 32x2 8x 1
1
y 2 (x 3)(x 2)
50. a.
b.
(0.5, 3.125)
1
(3, 0)
x
1
(2, 0)
x 0.5
y
3
(0, 0)
x1
As c increases, the graph moves upward. The graph
moves left as b increases.
(1, 3)
y 3x(x 2)
51.
(2, 0)
1
1
x
Torque (foot-pounds)
37.
38. y x 5x 2
y x2 5x 2x 10
y x2 7x 10
39. y x 3x 4
40. y 2x 1x 6
y x2 3x 4x 12
y 2x2 x 6x 6
y x2 x 12
y 2x2 14x 12
126
Algebra 2
Chapter 5 Worked-out Solution Key
y
80
75
70
65
60
55
50
45
40
0
x
0
1
2
3
4
5
6
Speed (thousands of revolutions per minute)
About 3093 rev per min; 74.68 foot-pounds
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
61. 6x 18 48
52. width 160 ft
6x 30
height 1.5 ft
53.
18x 11
x 11
18
x 5
y
90
Rate (calories per minute)
62. 20x 5 2x 6
63. 0.6x 0.2x 2.8
80
64.
0.4x 2.8
70
60
11x 11
40
2
x7
50
35x 24x 11
40
2
x 20
40
30
20
65.
10
0
0
50
75
100
125
150
Speed (meters per minute)
5x
x
1 1
12 6
4 2
3x
3
12
4
x
Sample answer: The energy use decreases until about 90
meters per minute and then increases.
54. width 6 ft
x 3
66.
z
(0, 0, 4)
height 2 ft
55. a. x xyz4
21.4
14%
1.522
(0, 4, 0)
y
y 0.761142 21.414 94.8 56 cm3 per gram
b. x 17.7
13.6%
1.304
x
y 0.65213.62 17.713.6 76.0 44 cm3 per gram
c.
Popping volume
(cm3/gram)
y
60 y 0.761x 2 21.4x 94.8
50
40
30
y 0.652x 2 17.7x 76.0
20
10
0
8 9 10 11 12 13 14 15 16 17 18 x
Moisture content
(% of weight)
2xh z
(0, 0, 3)
answer: Hotair popping
produces a
greater volume than hotoil popping.
x y 2z 6
(0, 6, 0)
y
x (6, 0, 0)
68.
z
y ax px q
56. y ax h2 k
x2
67.
d. Sample
Volume of Popcorn
y a
(4, 0, 0)
k
h2
y ax2 2axh ah2 k
3x 4y z 12
y ax2 xp xq pq
(0, 3, 0)
y ax2 axp q apq
For y ax 2axh k, a a and b 2ah.
b
Then x (the x-coordinate of the vertex)
2a
2ah
h. For y ax 2 aqx apq, a a and
2a
b
b ap q. Then x (then x-coordinate of the
2a
ap q p q
vertex) .
2a
2
2
x
69.
z
x2
59. 4x 28
x 7
Copyright © McDougal Littell Inc.
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(0, 0, 5)
5x 5y 2z 10
(0, 2, 0)
(2, 0, 0)
57. x 2 0
y
(4, 0, 0)
ah2
5.1 Mixed Review (p. 255)
(0, 0, 12)
y
x
58. 2x 5
x 2.5
60. 4x 8
x 2
Algebra 2
Chapter 5 Worked-out Solution Key
127
Chapter 5 continued
70.
z
75. A (0, 0, 14)
2x 7y 3z 42
(0, 6, 0)
y
x
71.
z
(0, 3, 0)
y
x 3y 3z 9
(0, 0, 3)
y
x (9, 0, 0)
1
72. A 5
x
y
1
19
1
1
6
1
5
1
; det A 1 5 6
1
1
19
6
1 19
3
6
19 5
4
6
z
23
1
; det A 8 3 11
4
2
6 ;
1
4
4
1
2
2
1 6
1 1
21
4 12 8 2 24 8 8 34
2
21
21
5
3
1
4
2
4 6
1 1
21
20 24 6 8 30 12 50 34
4
21
21
5
3
1
2
4
1 4
1
1
21
5 8 12 4 20 6 1 22
1
21
21
2, 4, 1
3, 4
73. A 2
1
1
det A 5 12 6 2 30 6 21
(21, 0, 0)
x
5
3
1
1
76. A 1
2
3
1
7
1
1 ;
5
5
1
2 4
20 2
x
2
11
11
det A 5 6 7 2 7 15 18 20 38
2
5
3
2
4 15
y
1
11
11
x
2, 1
74. A 71 102; det A 14 10 24
15 10
9
2
30 90
x
5
24
24
7 15
1 9
63 15
y
2
24
24
5, 2
y
z
5
7
28
3
1
7
38
1
1
5
25 84 49 28 35 105 60 98
1
38
38
1
1
2
5
7
28
38
1
1
5
35 10 28 14 28 25 17 17
0
38
38
1
1
2
3
1
7
38
5
7
28
28 42 35 10 49 84 105 123
6
38
38
1, 0, 6
128
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
3
1
2
2
77. A 6
9
9
1 ;
4
det A 8 27 108 81 4 72
x
143 149 292
3 9
1 1
2
4
292
11
45
56
6. x2 16 x 4x 4
7. y2 2y 1 y 1y 1
8. p2 4p 4 p 2p 2
9. q2 q qq 1
x40
y
11 9
45 1
56
4
292
2
6
9
360 99 3024 3645 112 264
292
2763 3493
2.5
292
z
2
6
9
3 11
1 45
2 56
292
12. 3x 1x 3 0
3x 1
x 3
x 13
14. v2 14v 49 0
x 2
4u2
13.
10
2u 12u 1 0
2u 1
2u 1
1
2
u 12
u
15. 5w2 30w 0
v 7v 7 0
5ww 6 0
v7
w0 w6
16. y x 1x 5;
17. y x 2x 4;
2, 4
1, 5
18. y x 1x 1;
1, 1
19. y x 52;
5
20. y 2x 4x 3;
21. y 3x 2x 2;
2
3,
4, 3
2
22. 2x 122x 8 96 96
4x2 40x 96
112 1215 132 99 180 1008
292
x20
x4
44 168 810 504 22 540
292
1022 1022
7
292
11. x 4x 2 0
10. x 3 x 1
4x2 10x 24 0
4x 12x 2 0
1235 1089 146
0.5
292
292
The width of the border is 2 ft.
5.2 Practice and Applications (pp. 260–263)
7, 2.5, 0.5
1
22 7 15
1 ft per hr
78.
14
14
14
23. x2 5x 4 x 4x 1
24. x2 9x 14 x 7x 2
25. x2 13x 40 x 5x 8
Lesson 5.2
26. x2 4x 3 x 3x 1
5.2 Guided Practice (p. 260)
27. x2 8x 12 x 6x 2
1. Sample answer: numbers where the value of the function
is zero
2. The x-term is negative and its absolute value is greater
than the absolute value of the constant term.
3. The student did not set the factors equal to zero.
x2 4x 3 8
x2 4x 5 0
28. x2 16x 51
cannot be factored
29.
a2
3a 10 a 5a 2
30.
b2
6b 27 b 9b 3
31.
c2
2c 80 c 10c 8
32. p2 5p 6 p 6p 1
33. q2 7q 10
cannot be factored
14r 72 r 18r 4
34.
r2
x 1x 5 0
35.
2x2
x10
36. 3x2 17x 10 3x 2x 5
x1
x50
x 5
4. x2 x 2 x 1(x 2
7x 3 2x 1x 3
37. 8x2 18x 9 4x 32x 3
38. 5x2 7x 2 5x 2x 1
5. 2x x 3 2x 3x 1
2
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Algebra 2
Chapter 5 Worked-out Solution Key
129
Chapter 5 continued
39. 6x2 9x 5
79. w2 12w 36 3w 36 w2 0
cannot be factored
19x 6 5x 22x 3
2w2 9w 0
41. 3k2 32k 11 3k 1k 11
w2w 9 0
40.
42.
10x2
14m 16 11m 8m 2
11m2
43. 18n2 9n 14 3n 26n 7
w 0 w 92
80. y x 2x 1;
4u 3 7u 3u 1
44.
7u2
45.
12v2
25v 7 3v 74v 1
46.
4w2
13w 27 cannot be factored
82. y x 7x 5;
2, 2
6x 9 x 3
0, 3
86. y 3
x2
4x 5
50. 4r2 4r 1 2r 12
y 3x 5x 1;
51. 9s2 12s 4 3s 22
5, 1
52. 16t2 9 4t 34t 3
53. 49 54.
7 10a7 10a
1
2,
56. 5
x 2 5x 2x 1
57. 2
1 23x 13x 1
9x2
4
mn 9
b. If m n 0, then m n. Substituting in mn 9,
nn 9, n2 9, and n2 9. There is no
such number such that n2 9. Therefore, x2 9 is
not factorable.
58. 3x2 18x 81 3x 92
59. 42y2 7y 15 42y 3y 5
4 2x5 2x 20 10
90.
60. 716a2 24a 9 74a 32
20 8x 4x2 20 10 0
61. uu 7
4x2 18x 10 0
62. 6tt 6
2x 102x 1 0
63. v2 2v 1 v 12
x
64. 2d2 6d 8
65. x 4x 1 0
m 53
72. 4a10a 1 0
74.
x2 9x 20 0
x 4x 5 0
76.
3y 8y 1 0
130
2x2 x 105
93.
3x 40 0
2x2
x 105 0
x 5x 8 0
2x 15x 7 0
x5
x7
1
2
2 3x
94.
3x2
x 22 95.
x 44 0
1
2 6x
3x2
2x 114
x 114 0
3x 11x 4 0
3x 19x 6 0
x4
x6
p 7 p 7
3y2 5y 8 0
y
p2 49 0
p 7p 7 0
x 14
x2 3x 40
x2
1
a 0 a 10
4x 12 0
8
3
60 ft
92.
x 4 x 5
77.
x 60
70. 3m 52 0
b 5 b 6
75. 16x2 8x 1 0
x 60x 675 0
x 54 x 12
n 49 n 49
73. 3b 5b 6 0
x2 615x 40,500 0
68. 4x 52x 1 0
k 12
71. 9n 49n 4 0
91. 375 x240 x 90,000 40,500
x 11 x 8
x 35 x 2
69. k 122 0
1
2
0.5 ft
66. x 11x 8 0
x 4 x 1
67. 5x 3x 2 0
8
89. a. m n 0
2
55. 81c2 198c 121 9c 112
x2
87. y x 82;
88. y 2x 1x 4;
60b 36 5b 6
25b2
85. y xx 3;
10
2
100a2
83. y x 2x 2;
7, 5
84. y x 102;
48. x2 4x 4 x 22
49.
4, 3
2, 1
47. x2 25 x 5x 5
x2
81. y x 4x 3;
y 1
78.
5q2 11q 2 0
5q 1q 2 0
q 15 q 2
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
96. a. Sample answer: There is only one square that is x by
x, 5 strips of x units, and 6 unit squares. The rectangle
measures x 3 by x 2.
b.
x
102. C
x 2x 2 x2 4x 4 x2 4x c
103. 2x2 11x 16 x2 3x
1 1 1
x2 8x 16 0
x 4x 4 0
x
x4 D
1
1
1
1
0 342 b4 8
104.
8 48 4b
40 4b
x2 7x 12 x 3x 4
10 b
1500 30 2x50 2x 375
97.
B
1500 1500 160x 4x2 375 0
4x2 160x 375 0
105.
2x 52x 75 0
x2
x
x 2.5
The border width is 2.5 ft.
x4
60x x2 800
98.
x2
x2 60x 800 0
x2 x2 8x 16 x2 4x 4
x 20x 40 0
0 x2 12x 20
x 20
0 x 2x 10
20 ft by 40 ft
x 10
99. R 200 2x60 x
The door is 8 ch' ih by 6 ch' ih.
R 2x 10060 x
100, 60
5.2 Mixed Review (p. 263)
100 60
20
2
106.
70 5x680 20x R
108.
1.37
35
20.0196
y 0.0196352 1.3735
y 24
4x 11
or
x 1.75 or
109.
x 2.75
5x 4 14
5x 4 14 or 5x 4 14
$57,600 R
x
x8
4x 9 2
4x 7
1002424 R
101. y 0.0196x2 1.37x
x 2 6 or x 2 6
4x 9 2 or 4x 9 2
34, 14
Price for each camera should be $480 and the maximum revenue is $57,600.
107. x 2 6
x 4 or
100x 34x 14 R
34 14
10
2
x 3
x 3 x 3
To maximize revenue, charge $80. Maximum revenue is
$12,800.
100.
x 42 x 22
5x 18 or
x 3.6
110.
111.
5x 10
or
7 3x 8; no solution
x 1 < 3 112.
3 < x 1 < 3
4 < x < 2
x 2
2x 5 ≤ 1
1 ≤ 2x 5 ≤ 1
4 ≤ 2x ≤ 6
2 ≤ x ≤ 3
Big Bertha could fire a shell about 70 miles with a
maximum height of about 24 miles.
Copyright © McDougal Littell Inc.
All rights reserved.
Algebra 2
Chapter 5 Worked-out Solution Key
131
Chapter 5 continued
113.
x 4 > 7
127.
128.
y
y
1
x 4 < 7 or x 4 > 7
114.
x < 3 or
1
3x 1 ≥ 2
1
3 x 1 ≤ 2
1
3 x ≤ 3
y x2 2
1
3x
or
(0, 2)
1 ≥ 2
1
3x
or
x ≤ 9 or
115.
x0
x ≥ 3
129.
116.
y
yx1
y
1
x0
y
(0, 3)
1
x
1
x
2
y x 2 3
1
1
1
x
130.
y
y 2x 3
1
(0, 5)
x0
≥ 1
3
1
y 2x 2 5
x
1
x
1
1
1
x > 11
1
1
y (x 1)2 4
(1, 4)
x
1
x 1
131.
117.
118.
y
y
1
1
1
1
x
1
(2, 1)
y (x 2)2 1
x
1
5
y 2x 7
y 3x 5
x2
y
1
1
1
x
1
132.
x 3
y
(3, 7)
y 3(x 3)2 7
119.
120.
y
y
1
1
1
xy4
x
1
1
1
1
1
2
2x y 6
x
1
133.
121.
122.
y
1
1
y
y
5x 3y 15
1
x
1
x
1 x
1
(0, 1) y 4 x 2 1
1
3x 4y 12
1
1
x0
1 x
134.
123.
124.
y
y
y2
x4
y
1
x
1
1
1
1
1
1
1
1
1
x
x
1
y 3
1
(4, 6)
125.
126.
y
135.
y
y
x 1
1
1
x4
1
1
x
1
1
1
Algebra 2
x y 22
2x 3y 50
2
y 3 (x 1)(x 3)
x
1
x
x1
Chapter 5 Worked-out Solution Key
136.
2
3
(1, 2 )
1
132
y 2 (x 4)2 6
222 y 3y 50
44 2y 3y 50
y6
You can take the bus
only 6 times.
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
Lesson 5.3
5.3 Practice and Applications (pp. 267–269)
Activity (p. 264)
19. 3
1. a. 36 6
21. 3
b. 8 22 2.8
9 6
4
2
4 22 2.8
23.
25.
c. 30 1.7
10 1.7
3
27.
1. a.–c. Sample answer: ab a
2. a.
49 32
4
9
c.
b.
29.
252 3.5
25
2
3
b
31.
33.
3.5
2
36.
19
39.
1.6
2. a.–c. Sample answer:
ab a
42.
b
44.
5.3 Guided Practice (p. 267)
1. Sample answer: to eliminate a radical from the denomi-
nator of a fraction
2. Sample answer: The product property says that the
square root of a product equals the product of the square
roots. The quotient property says that the square root of a
quotient equals the quotient of the square roots.
4. 7
3. 2; 1; 0
6. 5
8.
11.
9 35
16 4
25 5
52
2
77
2
9.
7. 3
7
3
10
2
3
3 9 9
7
10.
3
3
3
3
12. x2 64
13. x2 25
x ±8
x ±5
14. 4x2 16
3
48.
50.
x ± 23
4
3
40
169
x ± 10 1
16t2
50
8 16t2 50
42 16t
2
21
8
36
37.
3
25
40.
4
210
13
11
64
43.
6
5
38.
11
8
23
3
3
20
7
x2
17
235
7
517
17
45.
9
100
81
41.
1
3
10
9
75
36
53
6
23
3
5
52. x2 90
x ± 11
x ± 310
54. 2x2 36
36
x2
6
51. x2 121
x2 18
x ± 32
x ±6
55.
1
35.
5 30
5
5
144 11
7 2
14
1211
47.
11
4
11 11
8 2
18 13
45 2
310
326
49.
8
13
13 13
32 2
517
17
75
x2 75
x ± 53
56. 10u2 6
17. x 82 28
x 1 ± 10
2
7
u2 16. x 12 10
h
16
x ±2
18.
49
53. 3x2 108
3
15. x2 12
x2 4
46.
3 23
5. 4
2 2 2 3 3 12
34. 2
197 1.6
7
3 2 32 20. 2 2 2 2 3 43
3 3 33 22. 2 2 13 213
9 2 4 62 24. 25 7 57
49 2 72 26. 121 5 115
2 7 14 28. 4 2 2 4
3 3 4 6 30. 34 5 65 180
4 3 2 26 32. 2 3 2 5 215
43 3 7 127
6
10
u±
x 8 ± 27
x ± 27 8
57.
v2
25
60
10
12
±
15
5
58.
p2
10
8
v2 12 25
p2 8 10
v ± 103
p ± 45
t2
t
21
8
1.6 sec t
Copyright © McDougal Littell Inc.
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Algebra 2
Chapter 5 Worked-out Solution Key
133
Chapter 5 continued
59.
q2
72
2
2
q 144
60.
2x2 6x 9 8 0
68. s 12 24 75
s 12 99
2x2 12x 18 8 0
q ± 12
s 1 ± 311
2x2 12x 10 0
s 1 ± 311;
2x 2 6x 5 0
1 311, 1 311
2x 1x 5 0
0 16t2 177
69.
1, 5
16t2 177
61. 4x2 2x 1 100 0
4x2 8x 4 100 0
4x2 8x 96 0
70. a. h 16t2 20
4x 6x 4 0
b.
6, 4
62. 3x 22 18
x 22 6
x 2 ± 6
x 2 ± 6
2 6, 2 6
63. 5x 72 135
t
0
0.1
0.2
0.3
0.4
0.5
0.6
h
20
19.84
19.36
18.56
17.44
16
14.24
t
0.7
0.8
0.9
1.0
h
12.16
9.76
7.04
4
t
1.4
t2 7 33, 7 33
64. 8x 42 9
t
9
8
4, 4
a 62 49
a 6 ±7
a 6 ± 7;
20 5
16 4
5
2
Mars
0 16t 200
2
66. b 82 28
b 8 ± 27
b 8 ± 27;
8 27, 8 27
13, 1
67. 2r 5 81
2
2r 5 ± 9
2r 5 ± 9
r
16
71. Earth
4
65. 2a 62 98
7.04
t 1.1 sec
32
x 4 ±
;
4
4
0.64 3.04
1.3
16t2 20
x 7 ± 33;
32
1.2
0 16t2 20
x 7 ± 33
1.1
1.5
h 11.36
x 72 27
32
4
t 3.3 sec
4x2 2x 24 0
x4±
177
t
5±9
;
2
16t2 200
t
52
2
t 3.5 sec
6t2 200
t
203
6
t 5.8 sec
Jupiter
Neptune
81
0 t 2 200
2
81t2 400
0 18t2 200
18t2 200
t
400
81
t
200
18
t
20
9
t
20
6
t 2.2 sec
7, 2
0 6t2 200
t 3.3 sec
—CONTINUED—
134
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
71. —CONTINUED—
0 12.5 b.
Pluto
2.1 2
t 200
2
2
2.1t 400
0
t
400
2.1
t
202.1
2.1
0 12.5 2
83 t
1800
180012.5 83 t
180012.5
t
83
146.2 t
t 13.8 sec
about 146.2 sec
15 0.019s2
72.
2223 t
60 30
c. Sample answer: The water drains more slowly as the
time increases.
15
s
0.019
76.
y
y
77.
28.1 knots s
(2, 3)
73. 272 4x2 3x2
(1, 2)
1
272 16x2 9x2
1
x
1
272 25x2
272
x2
52
78.
y
79.
y
27
x
5
x
1
1 x
1
(1, 4)
21.6 in. by 16.2 in.
20 0.00256s2
74. a.
1
80.
88.4 s
y
81.
y
4
2
about 88.4 mih
b.
(3, 5)
2 x
20
s
0.00256
(4, 0)
40 0.00256s2
x
x
2
1
40
s
0.00256
(6, 2)
125 s
No; Sample answer: When P 40 lbft2, speed is
125 mih which is not 2 88.4.
c. Sample answer: The wind speed value is squared in
the formula and squaring increases the pressure value
quickly.
75. a.
12.5 25 12.5 5 22
t
60 30
83
t
1800
23
2
83
12.5 5 t
1800
6364 9000 83t
2636 83t
2
5
0
1
1
82.
181
84.
16
85.
20
105 77
81 57
24
40 18
0 49
40 31
83.
11
13
12 20
4
16 32
86. y x2 5x 2x 10
87. y x2 x 8x 8
y x2 3x 10
y x2 9x 8
88. y 2x2 7x 8x 28
y 2x2 15x 28
89. y 16x2 36x 36x 81
y 16x2 81
2636
t
83
60.6 t
about 60.6 sec
Copyright © McDougal Littell Inc.
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Algebra 2
Chapter 5 Worked-out Solution Key
135
Chapter 5 continued
90. y x2 3x 3x 9 1
2. y y x2 6x 10
91. y 5x2 6x 6x 36 12
y
y 5x2 60x 180 12
20.52 2 20.5222
x 16
32
0.252 2 0.252
x 16
8
y 0.1542x2 0.3084
y 5x2 60x 168
y
Quiz 1 (p. 270)
1.
x0
2.
y
y
1
1
x 2
x1
x 2
y
1
3 (x
y 0.1542x 2 0.3084
1
1
1
1 x
0 2 fx fR2xf fR
2 fx fR
x
(2, 3)
5)(x 1)
1 x
x
4. x 3x 9 0
x30
x 3
4t2 4t 1 0
6.
2t 12t 1 0;
x40
x 54
x 4
2t 1 0
t 12
10.
6 36
8. 72
2 5 145
365 365 55 6 5 5
4
3
R2
2
43 23
6
3
1. 1.53, 1.53
2. 1.73, 1.73
3. 2.45, 2.45
4. 2.87, 2.87
5. 2.73, 0.73
6. 0.90, 8.90
7. 3.65, 1.65
8. 0.85, 2.35
9.
6r2
48 8 r2
2.8 in. r
4
Technology Activity 5.3 (p. 271)
x9
5. 4x 5x 4 0
7. 54 9
fR
2 f
No, the x-intercepts are in terms of the radius only.
x90
4x 5 0
fR
R2
2
2 f
2fx fR
1
9.
0 22f 2x2 2f 2R2
3.
y
1
1
x
1
(0, 0.3)
y 2(x 2)2 1
(2, 1)
y x 2 2x 3
(1, 4)
3.
(1.4, 0)
(1.4, 0)
x
10 1.35s2
11.
Lesson 5.4
5.4 Guided Practice (p. 277)
10
s 2.7 mih
1.35
1. 3, 7i
2. Sample answer: The real part should be the
same and the imaginary part should be the
opposite of the given imaginary part;
5 2i.
Math and History (p. 270)
1. y 0; it is the x-axis.
3. Sample answer: distance from origin
4. x2 9
x ± 3i
5. 2x2 16
x2 8
x ± 2i2
136
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
6. x 1 ± i7
37. 2 3i 7 i 9 4i
7. 7 3i
38. 6 2i 5 i 11 i
x 1 ± i7
4 3i 2 4i 6 i
39. 4 7i 4 7i 8
9. 7 7i 2i 2 9 5i
40. 1 i 9 3i 8 4i
8.
10.
41. 8 5i 1 2i 7 3i
3 4i 1 i 3 4 7i 1 7i
1i
1i
2
2
11. 1 1 2
2
42. 2 6i 10 4i 12 10i
12. 0 3 3
2
2
2
43. 0.4 0.9i 0.6 i 0.2 0.1i
13. 22 32 4 9 13
44. 25 15i 25 6i 21i
14. 52 52 25 25 52
45. i 8 2i 5 9i 3 6i
15.
16.
imaginary
2 + 3i
3i
1+i
i
1
i
1
c 12 12
c 2
Sample answer: It does
not because the absolute
values become infinitely
larger.
real
55. 225 120i 120i 64 161 240i
20. 2x2 50
x2 25
x ± 5i
22. x2 18
15
50. 40 8i 5i 1 39 13i
54. 9 30i 30i 100 91 60i
x ± i11
x ± 3i3
21.
49. 40i 70 70 40i
53. 49 35i 35i 25 74
18. x2 11
x ± 2i
5x2
48. 4i6 i 24i 4 4 24i
52. 18 12i 81i 54 36 93i
5.4 Practice and Applications (pp. 277–280)
19. x2 27
47. i3 i 3i 1 1 3i
51. 11 22i i 2 9 23i
5 – 5i
17. x2 4
46. 30 i 18 6i 30i 12 23i
x2 3
56.
8 8i
4 4i
11
57.
2i 2
i 1 1 i
11
58.
5 3i 4i 20i 12 5i 3
3 5
i
4i
4i
16
4
4
4 4
59.
3 i 3 i 9 6i 1 8 6i 4 3
i
3i 3i
91
10
5 5
60.
2 5i 5 2i 10 10 25i 4i 20 21i
5 2i 5 2i
29
29
61.
7 6i 9 4i 63 26i 24
87 26
i
9 4i
9 4i
81 16
97 97
x2 18
x ± 3i2
x ± i3
23. 3r2 3
24. 4s2 1
r2 1
s2 14
r ±i
s ± 12i
25. t 22 16
26. u 52 20
t 2 ± 4i
u 5 ± 2i5
u 5 ± 2i5
t 2 ± 4i
27. v 3 56
28. w 42 9
1
2
w 4 v 3 ± 2i14
w 4 ± 13i
v 3 ± 2i14
29.–36.
1 + 5i
4 + 2i
2 i
1
i
1
real
6 3i
Copyright © McDougal Littell Inc.
All rights reserved.
10 i
10 i
17 62
i
19
19
66. 22 12 4 1 5
67. 72 12 49 1 50 52
3
4i
65. 52 122 25 144 169 13
5 + 4i
i
10 i
64. 32 42 9 16 25 5
imaginary
1 + i
1
± 3i
10
10 i10 10 10
i
10 1
11
11
6 i2 6 i2 36 2 12i2
63.
36 2
6 i2 6 i2
62.
68. 22 52 4 25 29
69. 42 82 16 64 80 45
70. 92 62 81 36 117 313
Algebra 2
Chapter 5 Worked-out Solution Key
137
Chapter 5 continued
71. 112 52 11 5 16 4
72. f z z2 1
z0 0
z1 f 1 12 1 2
z2 f 2 5 1 6
z3 f 5 25 1 26
z0 0
z1 2
z2 26
z3 626
Sample answer: No, because the absolute values become
infinitely large.
z1 f 0 1
z2 f 1 1 1 0
z3 f 0 1
z0 0
z1 1
z2 0
z3 1
Sample answer: It does because the absolute values are
equal to or less than N 1.
74. f z z2 i
z0 0
z1 f 0 i
z2 f i 0
z3 f 0 i
z0 0
z1 1
z2 0
z3 1
75. f z z2 1 i
z1 f 0 1 i
z2 f 1 i 2i
z3 f 2i 4 1 i
z1 0.5
z2 0.25
z3 0.4375
z4 0.3086
Sample answer: It does because the absolute values are
less than N 1.
z1 0.5i
z2 0.25 0.5i
z3 0.1875 0.25i
Sample answer: It does because the absolute values are
less than N 1.
z0 0
z1 2
z2 2
z3 26
81. false; Sample answer: 3 is irrational but not complex.
82. true
83. false; Sample answer: 6 3i 5 3i 1 which
is not imaginary.
84. false; Sample answer: Let the real number 4 5 i 2;
its complex conjugate is 5 i2 which is equal to 6;
4 6.
85. true
86. a.
76. f z imaginary
5 6i
5i
i
Sample answer: It does not because the absolute values
become infinitely large.
z2
z0 0
z1 0.5
z2 0.3125
z3 0.3125
z0 0
80. true
Sample answer: It does because the absolute values are
less than N 2.
z0 0
z0 0
z1 0.5
z2 0.25
z3 0.4375
z4 0.3086
z0 0
79. f z z2 0.5i
73. f z z2 1
z0 0
78. f z z2 0.5
1
i
1 3
5 real
2
2
z0 0
z1 2
z2 6
z3 38
z4 1446
z0 0
z1 2
z2 6
z3 38
z4 1446
Sample answer: It does not because the absolute values
become infinitely large.
77. f z z2 1 i
z0 0
z1 1 i
z2 2i
z3 5 i
z4 24 10i
z0 0
z1 2
z2 2
z3 26
z4 26
2 i 3 5i 5 6i
b.
imaginary
7
4i
6i
6 2i
1
i
1
real
1 6i 7 4i 6 2i
87. true; true
88. true; false
90. true; true
91. false; false
89. false; false
92. no
Sample answer: It does not because the absolute values
become infinitely large.
138
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
5.4 Mixed Review (p. 280)
93. Sample answer: Geometric: in both definitions, the
absolute value is the distance from the point to the origin;
algebraic: a real number can be written as a 0i. Then
z a2 02 a2 a. The absolute value of a
real number a is 0, a, or a and always positive.
3 3i
b. 3 i;
10
1i
94. a. 1 i;
2
c. 2 8i;
101. f 3 43 1 12 1 11
102. f 4 42 54 8 16 20 8 44
104. f 30 2
105. A 2 8i
1
2
i
68
34 17
35
A1 95. a. 2 5i 7i 2 2i
b.
12 8i 15i 12 7i
1
2
1
2
6 5 5
18 8 18i 26 18i
Z
9 2i
9 2i
106. A 17
A1 Z
270 110i 54 22
i
85
17 17
xy 78
Z
40 27 21i 67 21i
13 6i
13 6i
Z
67 21i 13 6i 871 126 129
13 6i
13 6i
169 36
107. A Z
10 28 6i 38 6i
7 3i
7 3i
Z
38 6i 7 3i
7 3i
7 3i
108.
97. 25 16 41 or 9 36 45 35
1
1
212 57
2 0.52 3 0.25 3.25
i5
i6
i7
A
8
i
1
5
1
10
10
4
0
3
109. x2 4x 4 36 0
x2 8x 15 0
x2 4x 32 0
x 3x 5 0
x 4x 8 0
3, 5
110.
B
x2
4, 8
22x 121 25 0
x2 22x 96 0
111. x 52 10
x 5 ± 10
x 5 ± 10
112. x 72 12
x 7 ± 23
x 7 ± 23
113. 3x 6 21
2
i 1 i 1
b. Sample answer: The pattern is i, 1, i, 1;
i9 i, i10 1, i11 i, i12 1
c. i26 i2 1; i83 i3 i
2
5
3
10
1
5
1
10
2
6, 16
99. 22 22 4 4 22 or
Simplified
form
i 1 i 1
2
5
3
1
10
x 6x 16 0
C
i4
x 42 1 0
98. 36 64 100 10 or
Copyright © McDougal Littell Inc.
All rights reserved.
4, 3
266 18 156i 248 156i 124 78
Z
i
49 9
58
29
29
Power of i
1
1
1
4
4 6 3
xy c. Z1 2 4i, Z2 5 7i
i3
1
8
1
7
2
4
13
A1 997 129i
Z
205
i2
1
8
8 7 7
5, 7
b. Z1 5 3i, Z2 8 9i
i1
59 12
26 18i 9 2i 234 36 110i
9 2i
9 2i
81 4
100. a.
1
8
Z
1
3
1, 2
96.a. Z1 3 4i, Z2 6 2i
3
1
2
3
5
1
3
xy 52
c. 2i 8 6i 4i 8 4i
102 100 10
103. f 9 9 6 3 3
x 62 7
x 6 ± 7
x 6 ± 7
Algebra 2
Chapter 5 Worked-out Solution Key
139
Chapter 5 continued
Number of DVD players sold
(in thousands)
114.
y 35.33x 14.58
N
450
12. x2 16x 64 12 0
x 82 12
350
x 8 ± 2i3
x 8 ± 2i3
250
13. x2 8x 16 7 0
150
50
0
x 42 7
N 35.33t 14.58
0
3
6
9
x 4 ± 7
12 t
x 4 ± 7
Time (in months)
x2 6x 2 0
14.
Lesson 5.5
x2 6x 9 11 0
Developing Concepts Activity 5.5 (p. 281)
1.
Expression
x2
x2
x2
x2
x2
2x 1
4x 4
6x 9
8x 16
10x 25
1
2. a. d 2 b
Number of 1-tiles
needed to complete
the square
1
4
9
16
25
x 32 11
Expression
written as
a square
x 12
x 22
x 32
x 42
x 52
x 3 ± 11
x 3 ± 11
15.
x2
4x 4 27
x 22 27
x 2 ± 3i3
x 2 ± 3i3
y x2 12x
16.
y 36 x2 12x 36
b. c d2
y x 62 36;
c. Find the square of half of the coefficient of the second
6, 36
term.
17.
5.5 Guided Practice (p. 286)
y 7 x2 4x
y 7 4 x2 4x 4
1. Sample answer: Write the expression as a square of a
y x 22 3;
binomial.
2, 3
2. Sample answer: completing the square since not every
y 31 x2 8x
18.
quadratic equation can be solved by factoring
y 31 16 x2 8x 16
3. Sample answer: The number 9 should have been added
to the left side since 19 9; y x 3 13.
2
4. 1; x 1
5. 49; x 7
6. 9; x 3
7. 25; x 5
2
y x 42 15;
2
2
2
8.
25
4;
x 10.
x2
4x 1 0
x2
4x 4 3
5 2
2
9.
169
4 ;
x 4, 15
y 17 x2 10x
19.
13 2
2
y 17 25 x2 10x 25
y x 52 8;
5, 8
x 2 3
2
y 45 x2 14x
20.
x 2 ± 3
y 45 49 x2 14x 49
x 2 ± 3
x2
11.
2x 4 0
x 2x 1 5 0
2
x 12 5
x 1 ± 5
x 1 ± 5
140
y x 72 4;
Algebra 2
Chapter 5 Worked-out Solution Key
7, 4
21.
y 4 2x2 2x
y 4 2 2x2 2x 1
y 2x 12 6;
1, 6
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
x60 2x 140
22.
51. u2 6u 9 35 9
u 32 44
60x 2x2 140
u 3 ± 211
x2 30x 70
x2
u 3 ± 211
30x 225 70 225
x 15 155
52. v2 30v 225 243 225
2
v 152 18
x 15 ± 155
v 15 ± 3i2
x 15 ± 155
v 15 ± 3i2
x 27.5 or x 2.6
53. m2 1.8m 0.81 1.5 0.81
60 55 5
m 0.92 2.31
27.5 ft by 5 ft
m 0.9 ± 2.31
m 0.9 ± 2.31
5.5 Practice and Applications (pp. 286–289)
23. x 82
24. x 102
27. x 0.5
30. x 25. x 122
29. x 28. x 0.7
2
2
31.x 1 2
12
33. 81; x 9
2 2
9
2
x 92 2
x 232 2
81
4;
529
4 ;
37.
39.
121
4 ;
225
4 ;
x 112 2
x 152 2
41. 8.41; x 2.92
42. 0.64; x 0.82
43. 22.09; x 4.72
46.
x 17 2
2
x 17
16 1
49 ;
289
256 ;
45.
25
9;
2
n 23
n 23
56.
x2
x2
x2
14x 49 50 49
x 7 ±i
x 7 ± i
58.
3
x
2
x
13
4
3 ± 13
2
2
x
3 ± 13
10x 70
x 52 45
x 5 ± 3i5
x 102 4
2
x2
x2 10x 25 70 25
20x 100 104 100
9
9
1
4
4
14x 50
x 72 1
x 6 ± 22
50. x2 3x x 3 ± 2
x 4 ± 7
x 6 ± 22
x 10 ± 2i
x 32 2
x 4 ± 7
x 1 ± 10
x 10 ± 2i
± 2
6x 9 7 9
8x 16 9 16
x 53 2
x 1 ± 10
49.
2
x2
x 42 7
x 12 10
x2
x2 6x 7
55.
8x 9
x2
57.
x 62 8
4
14
9 9
x 3 ± 2
47. x2 2x 1 9 1
48. x2 12x 36 28 36
4
9
n 23 ± 2
40. 0.01; x 0.12
44.
32. 36; x 62
35. 484; x 222
38.
4
54. n2 3 n 34. 169; x 13
2
36.
26. x 192
3 2
2
59.
x 5 ± 3i5
13
r2 5r 4
r2 5r 13 25
25
4
4
4
r 25
r
2
3
5
± 3
2
r
5 ± 23
2
2
Copyright © McDougal Littell Inc.
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Algebra 2
Chapter 5 Worked-out Solution Key
141
Chapter 5 continued
2s2 26s 1
60.
k2
169 1 169
4
2
4
s2 13s 5k2 10k 155
69.
2k 1 31 1
k 12 32
s 132 171
4
2
k 1 ± 42
13
319
s
±
2
2
s
61. t2 t t 21
70.
b 35
p2 22p 290
71.
p2
22p 121 290 121
p 112 169
1
4
p 11 ± 13i
1
i
t ±
2
2
r
30b 9 0
5b 35b 3 0;
13 ± 319
2
1
1 1
4
2 4
2
k 1 ± 42
25b2
p 11 ± 13i
72.
1 ± i
2
5q2
9q2
360
4q2
360
q2
w2 12w 52
62.
w2 12w 36 52 36
73.
w 62 16
y x 32 2;
w 6 ± 4i
3, 2
6, 2
74.
64. x2 6x 9 15 9
y x 12 10;
x 3 ± 26
1, 10
x 3 ± 26
75.
65. 9x2 23
y 14 x2 16x
y 14 64 x2 16x 64
23
9
x±
y 9 x2 2x
y 9 1 x2 2x 1
x 32 24
x2 y 11 x2 6x
y 11 9 x2 6x 9
w 6 ± 4i
63. x 6x 2 0;
90
q ± 3i10
y x 82 50;
8, 50
23
3
76.
66. 2x 7x 1 0;
72,
1
y 68 x2 26x
y 68 169 x2 26x 169
3x x 6
2
67.
1
1
72
1
x2 x 3
36
36 36
1
x
6
2
y x 132 101;
13, 101
77.
71
36
9
9
y 2 4 x2 3x 4
1± i71
6
68. x 82 36
x 8 ±6
y x 32 17
4;
2
i71
1
x ±
6
6
x
y 2 x2 3x
32, 174 78.
y 1 x2 7x
y1
49
4
x2 7x 49
4
y x 72 53
4;
2
72, 534 x 8 ± 6;
14, 2
142
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
y 80 x2 20x
79.
88.
y 80 100 x2 20x 100
x2 5x y x 102 20;
10, 20
y 47 x 14x
y 47 49 x2 14x 49
x
y x 7 2;
2
7, 2
y 1 12 3x2 4x 4
y 3x 22 11;
s2 13.75s 1000
s2 13.75s 47.3 1047.3
s 6.8752 1047.3
y 2x 12 2 13
2
s 6.875 ± 1047.3
s 6.8751047.3
s 25.5
y 3 5.6 1.4x2 4x 4
y 1.4x 22 2.6;
2, 2.6
2
3
2
3
2
3
y
65x
9
y x2 65x 25
2
6
y x 35 25
;
3
6
5 , 25
85.
d 0.08302 1.130 105 ft
y 3 1.4x2 4x
83.
x2
256
5 241
2
80 0.08s2 1.1s
y 7 2x2 x
12, 132 241
4
241
5
±
2
2
89.
y 7 12 2x2 x 14
84.
x 10.26
2, 11
82.
2
x
y 1 3x2 4x
81.
25
25
54 4
4
x 25
2
80.
xx 5 54
about 25.5 mi
h
90.
0.0241x 2 41.5x 228.2 0
0.0241x 2 41.5x 430.6 658.8 0
0.0241x 20.752 15.9
x 20.752 659.75
x 20.75 ± 659.75
100 xx 10
x 20.75 659.75
100 25 x2 10x 25
x 46.4
125 x 52
± 55 x 5
x 5 55
x 6.18
40 12x 8x
86.
80 x2
8x
80 16 x 8x 16
2
96 x 42
Her throw was about 46.4 ft.
91.
y 0.003x2 0.62x 3
25 3 0.003x2 206.7x
10,681 7333 x2 206.7x 10,681
3348 x 103.352
± 3348 x 103.35
± 693 103.35 x
x 45.5 ft or x 161.2 ft
± 46 x 4
46 4 x
x 5.8
87.
1
2 4xx
4 70
2x2 8x 70
x2 4x 4 35 4
x 22 39
x 2 ± 39
x 2 39
x 4.24
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Algebra 2
Chapter 5 Worked-out Solution Key
143
Chapter 5 continued
92. a. 4l 3w 240
3w 240 4l
w 80 y 3 8 2x2 4x 4
y 2x 22 5;
4l
3
A
4l2
1000 80l 3
b.
y 3 2x2 4x
98.
99. a.
b.
y
y
y (x 2)2
4
1000 l2 60l 3
1
1
4
1000 1200 l2 60l 900
3
1
y x 2 2x
y x 2 4x
c.
± 150 l 30
30 ± 150 l
y
y (x 3)2
42.25 ft by 23.67 ft or 17.75 ft by 56.33 ft
2
2
2
l 42.25 ft or l 17.75 ft
200 x 329 329 x
x
1
x
1
4
200 l 302
3
93.
y (x 1)2
x
2
y x 2 6x
200 9x2 6x 9 99 x
200 9x2 6x 9 9 x
100. Sample answer: The vertex moves down from the position
of the other vertex.
200 9x2 7x
200 49
49
x2 7x 9
4
4
800 441
7
x
36
2
± 4.4 x 2
101. 52 412 25 8 17
102. 82 437 64 84 20
103. 02 452.6 202.6 52
7
2
104. 42 4111 16 44 60
x 3.5 4.4 0.9 about 1 cm
105. 242 4169 576 576 0
106. 22 41.40.5 4 2.8 1.2
y 0.0267x2 30x
94.
5.5 Mixed Review (p. 289)
y 6 0.0267x2 30x 225
107. y 1 2x 3
108. y 4 x 2
y 2x 5
yx6
y 6 0.0267x 152
y 0.0267x 15 6
2
vertex 15, 6
The kangaroo can jump about 30 ft and 6 ft high.
109. y 10 5x 7
5.15q1.24 0.00002T 1015T257,556.25
2
y 3x 32
y 5x 25
111. y 9 3 x 6
112. y 2 4 x 11
y 13x 7
y 54x 47
4
5
1
q 0.00002T2 0.0203T 1.24
95.
110. y 8 3x 8
113.
q 3.9 0.00002T 507.52
114.
x2
y
y3
y
y2
q 0.00002T 507.52 3.9
1
507.5, 3.9
1
1
1
507.5 ft; 3.9 Btuft3
1
1
x
x
1
y 1
96. C
97. x2 12x 36 61 36
115.
xy4
x2 12x 36 25
x 62 25
x 6 ± 5i
x 6 ± 5i
116.
y
1
1
1
y yx2
1
x
1
1
1
x
x 3y 6
1
x0
B
144
Algebra 2
Chapter 5 Worked-out Solutions Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
117.
118.
y
16. h 16t2 v0t h0
y
y 2x 3
1
1
x
1
0 16t2 21t 6
1
3x 2y 8
1
1
2x y 0
1
x
y 2x 3
Technology Activity 5.5 (p. 290)
1. min; 4.25; 2.5
2. max; 5; 4
3. min; 4; 3
4. min; 5; 4
5. max; 8.125; 0.75
6. max; 2.125; 3.75
7. min; 2.375; 3.75
8. min; 4; 1
9. max; 8.65; 2.3
10. max at 80 cars per mile
and 1997 cars per hour
Lesson 5.6
5.6 Guided Practice (p. 295)
1. the discriminant
2. 2 real; 1 real; 2 imaginary
3. Sample answer: when an object is thrown upward
4 ± 42 413 4 ± 16 12
4. x 2
2
4 ± 4 4 ± 2
2
2
x 3 or 1
1 ± 1 4 1 ± 5
5. x 2
2
3 ± 9 40 3 ± 31
6. x 4
4
6 ± 36 36 1 ± 2
7. x 18
3
8 ± 64 4
8. x 4 ± 15
2
9. x 4 ± 16 4437 4 ± 576
8
8
4 ± 24i 1
± 3i
8
2
10. 25 412 25 8 17
2 real
11. 22 415 4 20 16
2 imaginary
12. 4 441 16 16 0
2
one real
13. 3 427 9 56 47
t
21 ± 212 4166
32
t
21 ± 441 384
32
t
21 57
32
t 0.42
0.42 sec
5.6 Practice and Applications (pp. 295–297)
17. x x
5 ± 25 56
2
x
5±9
2
7, 2
18. x 14. 144 494 144 144 0
1 real
3 ± 32 412
2
x
3 ± 9 8
2
x
3 ± 17
2
19. x x
2 ± 4 414
2
2 ± 4 16
2
x 1 ± 5
20. x x
10 ± 100 88
2
10 ± 12
2
x 5 ± 3
21. x x
6 ± 36 232
2
6 ± 14i
2
x 3 ± 7i
23. x 2
2 imaginary
5 ± 52 4114
21
x
3 ± 9 20
10
3 ± 29
10
22. x 7 ± 49 76
2
x
7 ± 3i3
2
x
7 ± 3i3
2
24. x 11 ± 121 48
6
x
11 ± 13
6
4, 1
3
15. 12 4513 1 260 261
2 real
Copyright © McDougal Littell Inc.
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Algebra 2
Chapter 5 Worked-out Solution Key
145
Chapter 5 continued
25. x x
1 ± 1 8
4
26. p 1 ± i7
4
p
8 ± 64 72
12
8 ± 2i2
12
2 i2
p ±
3
6
27. q 2 ± 4 252
14
28. r 16 ± 62
2
r
1 3
± i
4 4
9 ± 81 48
8
8 ± 64 40
20
8 ± 226
v
20
2
± 3i
3
v
2 26
±
5
10
32. x2 4x 20 0
x
4 ± 16 80
2
x
4 ± 8i
2
x 2 ± 4i
33. x2 2x 99 0
34.
6 ± 36 24
6
x
6 ± 23
6
x 1 ±
39.
8x2
8 ± 64 32
16
x
8 ± 46
16
x
1 6
±
2
4
40. 6x2 4x 1 0
x
4 ± 16 24
12
4 ± 210
12
x
2 ± 20
2
x
x
10 ± 100 56
2
10 ± 211
2
x 5 ± 11
35. x2 8x 35 0
3
x
x
10x 14 0
3
8x 1 0
2 ± 4 396
2
x
1 10
±
3
6
41. 4x2 40x 101 0
x
40 ± 1600 1616
8
x
40 ± 4i
8
x5 ±
i
2
42. 36k2 24k 5 0
x
8 ± 64 140
2
k
24 ± 576 720
72
x
8 ± 2i19
2
k
24 ± 12i
72
x 4 ± i19
146
x
x
x 11 or 9
x2
x 8 ± 32
38. 3x2 6x 2 0
9 ± 33
8
12 ± 54i
u
18
u
37. x2 16x 46 0
x
9
7
31. v 3 ± 37
2
4 ± 12i
16
1,
12 ± 144 3060
18
x
16 ± 256 184
2
r
30. u 3 ± 9 28
2
x
2 ± 16
14
t
x
4 ± 16 160
16
q
29. t 36. x2 3x 7 0
Algebra 2
Chapter 5 Worked-out Solution Key
k
1
i
±
3 6
Copyright © McDougal Littell Inc.
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Chapter 5 continued
54. 9v2 36v 31 0
43. 9n2 12n 5 0
n
12 ± 144 180
18
v
36 ± 1296 1116
18
n
12 ± 18
18
v
36 ± 180
18
n
1
5
or 3
3
v2 ±
44. 3d2 10d 1 0
d
10 ± 100 12
6
p
19 ± 361 168
28
d
10 ± 222
6
p
19 ± 23
28
d
5 ± 22
3
p
1
3
or p 7
2
y
56. 16 40 24; 2 imaginary
9.5 ± 90.25 127.92
7.8
9.5 ± 218.17
y
7.8
2
46. 6x 2 0
48.
57. 9 24 33; 2 real
58. 196 196 0; 1 real
59. 100 60 160; 2 real
60. 256 256 0; 1 real
61. 25 32 7; 2 imaginary
x ± 2
x2
x
3 ± 9 60
2
x
3 ± 69
2
62. 0 84 84; 2 real
63. 1 20 19; 2 imaginary
64. 400 400 0 1; real
65. zero
4x 4 29 4 49. x 16x 2 0
x 22 25
68.
x 2, 16
x 2 ± 5i
x 2 ± 5i
50. 4
x2
7x 4x 3
55. 14p2 19p 3 0
45. 3.9y2 9.5y 8.2 0
47.
5
49 49
49
4
7 2
2
70.
0
x
7
2
51. x 42 9
x 4 ± 3i
72.
x 4 ± 3i
x2
66. negative
67. positive
2x c 0
69. x2 4x c
a. c < 1
a. c < 4
b. c 1
b. c 4
c. c > 1
c. c > 4
x2
10x c 0
71. x2 8x c 0
a. c < 25
a. c < 16
b. c 25
b. c 16
c. c > 25
c. c > 16
x2
6x c 0
73. x2 12x c 0
a. c < 9
a. c < 36
52. 5u2 10u 5 0
b. c 9
b. c 36
u2 2u 1 0
c. c > 9
c. c > 36
u2
2u 1 1 1
u 1 2
2
u 1 ± 2
u 1 ± 2
53. 4m2 3
3
m2 4
m±
3
74. Sample answer: The initial velocity substituted into the
formula can be zero.
75. 0 16t2 5t 92
t
5 ± 25 5888
32
t
5 5913
32
t 2.56 sec
2
Copyright © McDougal Littell Inc.
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Algebra 2
Chapter 5 Worked-out Solution Key
147
Chapter 5 continued
76.
1
77 7x 11 xx
3
0 x2 18x x
18 ±
77
3
0 16
324 308
3
0
2
x9 ±
77. 0 2
b. t 10 ftsec 3.16 sec
55t 10
Sample answer: If t 2 sec then v0 would need to be
equal to v0 3222 112 ftsec.
5.6 Mixed Review (p. 298)
55 ± 3665
x
32
l
3x > 6
7x ≥ 21
x > 2
x ≤ 3
3s 22
0
0.1s2
s
3 ± 9 791.2
0.2
s
3 ± 800.2
0.2
2x ≤ 26
3s 1978
4x < 4
x ≥ 13
89.
x < 1
4 ≤ 5x 11 ≤ 29
15 ≤ 5x ≤ 40
3 ≤ x ≤ 8
s 156.4 ftsec
90.
79. $60 0.560t2 0.488t 51
3
2x
20 ≤ 14
3
2x
0 0.56t2 0.488t 9
91.
1 > 8x
or
≤ 6
x ≤ 4
0.488 ± 0.24 20.16
t
1.12
7 > x
or
or
7 < x
92.
y
0.488 ± 20.4
1.12
in the year 1993
y 2x
1
1
x
1
93.
h0 0 ft
94.
y
0 16t2 350t
1
1
16t 350
1
x
1
y 3x 2
1
1
t 21.875 sec
25 16 41
82. 4k2 4 4k2 1
2.7
y
1
0 t16t 350
83. 3.6
x
1
yx
80. a. v0 350 ftsec
81. 36 4 40
y
1
1
1
t 3.6
b.
88. 4x 3 < 1
87. 2x 18 ≤ 8
2000 0.1s2 3s 22
t
86. 16 7x ≥ 5
85. 3x 6 > 12
x 0.17 sec
78.
v02
160
64
3210 ftsec v0
55 ± 3025 640
x
32
0.1s2
v02
v2
0 160
1024
32
16064 v02
664
3
x 1.57 in.
16t 2
v0
;
32
84. a. maximum height occurs when t 9 4k2
B
B
A
95.
2x 3y 12
1
x
x
1
96.
y
1
1
1
xy5
y
x
1
1
7x 4y 28
148
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
97.
98.
y
32 72 94 494 11.
x2
2
y x 3
(0, 2) y x 2
 
1
1
1
(3, 0) x
1
1
58
2
x 42 2
x
x 4 ± 2
x 4 ± 2
y
1
12.
(0, 1)
1
2
8x 16 14 16
1
1
1
99.
10.
y
2x 1 17 1
x2
x 12 16
x
y 2x 1
x 1 ± 4i
x 1 ± 4i
13.
100.
p2
10p 25 27
p 52 27
y
p 5 ± 33
p 5 ± 33
1
y 3x 4
(4, 0)
5q2
14.
1 x
1
5
q2
20q 19
4q 4 19 20
5q 22 1
101.
102.
y
q 22 y
1
y x 2 3
x
1
q2±
1
y 2 x 5 4
(2, 3)
1
5
5
5
1
1
1
q 2 ±
(5, 4)
1 x
1. 5 16i
y 1 9 x2 6x 9
2. 4 10i
y x 3)2 8
3. 24 7 6i 8i 31 22i
4.
5
y 1 x2 6x
15.
Quiz 2 (p. 298)
5
y 50 x2 18x
16.
1 3i 5 i 5 3 15i i
5i
5i
25 1
y 50 81 x2 18x 81
y (x 92 31
1 8i
13
y 7 2x2 4x
17.
y 7 8 2x2 4x 4
y 2x 22 1
imaginary
5.–10.
2 + 4i
18. x 3 i
4 + 1i
i
1
i
4
1
x
real
2 ± 4 40
2
2 ± 211
2
x 1 ± 11
3
2
7
i
2
19. x 5i
5. 22 42 4 16 25
6. 52 5
8. 4 3 16 9 5
2
Copyright © McDougal Littell Inc.
All rights reserved.
16 ± 6i
2
x 8 ± 3i
7. 32 12 9 1 10
2
x
16 ± 256 292
2
9. 4 4
2
Algebra 2
Chapter 5 Worked-out Solution Key
149
Chapter 5 continued
20. w2 3w 4 0
7.
w
3 ± 9 16
2
w
3 ± i7
2
w
y x 2 2x 4
1
1
1
x
y x 2 3
3 ± i7
2
21. 25y2 40y 8 0
y
y
8.
40 ± 1600 800
50
y
y x 2 2x 4
1
40 ± 206
y
50
1
1
x
y x 2 3
4 ± 26
y
5
22. 4 16t2 15t 3
9.
0 16t2 15t 1
y
y x 2 2x 4
15 ± 225 64
t
32
1
1
1
15 ± 161
t
32
x
y x 2 3
t 0.86
about 1 sec
10. x2 4 < 0
11. x2 4 ≥ 0
x2 < 4
x2 ≥ 4
Lesson 5.7
2 < x < 2
5.7 Guided Practice (p. 303)
1. Sample answer: one variable: x2 5x 7 > 0
x2
12.
two variables: y ≥ x2 5x 7
x2
2. Sample answer: y ≥ x2 includes points on the graph of
a dotted line; find the y-intercepts and determine where
the solutions lie on the x-axis; algebraic: factor
x2 3x 4 and graph the critical x-values on a number
line; determine where the solutions lie on the number
line.
4.
5.
y
13. y 0.00211x2 1.06x
0 0.00211x2 1.06x 52
y
1
1
1
1
x
1.06 ± 1.1236 0.4389
0.00422
x
1.06 ± 0.6847
0.00422
x 55.1 m and 447.3 m
1
y 2x 2
1
3x 4 > 0
x < 1 or x > 4
1
y x2 2
x
x
5.7 Practice and Applications (pp. 303–305)
14. B
15. C
17.
6.
4 > 3x
x 1x 4 > 0
y x2 while y > x 2 does not.
3. Sample answer: graphical: Graph y x2 3x 4 using
x ≤ 2 or x ≥ 2
16. A
18.
y
y 3x 2
1
1
1
1
1
x
1
y x 2
x
1
y
150
y
1
y
x2 5x 4
Algebra 2
Chapter 5 Worked-out Solution Key
1
1
1
x
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 5 continued
19.
20.
y
31.
y
y
y x 2 5
y x 2 6x 9
1
1
1
1
1
y x 2 6x 3
x
1
21.
x
1
y x 2 3x
22.
y
1
1
y
x
1
y x 2 x 6
32.
y x 2 4x 4
1
y x 2 8x 16 11
1 x
y x 2 2x 1
1
1
1
23.
24.
y
y 2x 2 x 3
1
1
33.
x
1
y
2
x
1
1
x
1
y
1
1
y
1
x
2
1
y 3x 2 2x 5
x
2
2
y 2x 2 2x 5
y 2x 2 1
25.
y
1
1
1
x
1
34.
y 3x 2 5x 4
y 2x 2 9x 8
y
y x 2 6x 4
1
1
26.
x
1
y
1
y 2 x 2 2x 4
35.
36.
y
y
1
1
1
x
1
1
1
1
27.
28.
y
1
x
x
y
y = x2 x 2
y = 2x 2 7x 3
4
y 3 x 2 12x 29
1
1
1
2
x
1
1
2 < x < 1
x
y 0.6x 2 3x 2.4
37.
x ≤
38.
y
y x 2 2x 8
29.
30.
y
1
1
2
y
3x 2
y x2
1
y
y x2 x 5
1
x
1
y x2 3
1
1
or x ≥ 3
y
1
1
1
2
4
x
x
x
Copyright © McDougal Littell Inc.
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1
y 2 x 2 5
x ≤ 4 or x ≥ 2
1.8 < x < 2.8
Algebra 2
Chapter 5 Worked-out Solution Key
151
Chapter 5 continued
39.
49.
y
w
240
200
160
120
80
40
0
y 3x 2 24x 41
x2 3x 18 ≥ 0
w
25h2
703
0 10 20 30 40 50 60 70 80 90 h
Height (in.)
x 3x 6 0
0.125x2 569x 448,000 ≥ 0
x 3 or x 6
b. Decreases; there is an over supply of timber.
Value (dollars per
million board feet)
x ≤ 6 or x ≥ 3
43. 4x2 < 25
3x 1x 5 0
x2 1
x 5 or x 3
25
4
5
x ±
2
5
5
< x <
2
2
1
≤ x ≤ 5
3
x2
2x2
12x 32 < 0
45.
475
350
125
0
425x 2 42,500x 1,011,000 > 0
4x 5 > 0
4 ± 16 40
4
39 < x < 61
x
x 8 or x 4
x 0.9 or x 2.9
x < 8 or x > 4
x < 0.9 or x > 2.9
1 2
x 3x 6 ≤ 0
2
3 ± 9 12
1
no real solutions
47. Manila Rope
400 600 800 1000 1200 1400 1600 1800 2000 2200 x
Volume of timber (millions of board feet)
51. 425x 2 42,500x 761,000 > 250,000
x 8x 4 0
x
y
700
I
301,500
Average income (dollars)
46.
19h2
703
a. 400 ≤ x ≤ 1012.6
42. 3x2 16x 5 ≤ 0
44.
w
50. 0.125x2 569x 848,000 ≥ 400,000
40. no real solutions
41.
121–160 lb
Healthy Weights
x
Weight (lb)
1
(60, 259,000)
(40, 259,000)
267,500
233,500
199,500
165,500
Wire Rope
131,500
Weight for Manila Rope
0
w
20,000
1000
0
1.5
0.5
1.0
Diameter (in.)
d
15,000
52. a.
10,000
5000
0
0
1.5
0.5
1.0
Diameter (in.)
48. no; yes
20
(70, 131,500)
30 40 50 60 70 80 A
Age (years)
about 39 to 61 years
w 8000d 2
d
Reaction Times
Reaction time
(milliseconds)
w 1480d 2
2000
Weight (lb)
Weight (lb)
w
3000
0
(30, 131,500)
Weight for Wire Rope
y
30 V(x) 0.005x 2 0.23x 22
25
20
15
10
A(x) 0.0051x 2 0.319x 15
5
0
16 21 26 31 36 41 46 51 56 61 66 71 x
Driver’s Age (years)
b. Sample answer: Ax is always less than Vx.
c. Sample answer: siren; since audio stimuli reaction
time is less than visual stimuli reaction time
152
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
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Chapter 5 continued
53. a. y ≤ xx 4
b. y ≥ x 5x 1
0 ≤ x ≤ 4
y ≤ 3
y 22 4
h 12
y4
b7
A
A
2
3 44
32
3
z
A 23127 56
y3
61. A 1
y x 2 4x
1
1
1
x
5.7 Mixed Review (p. 305)
2y 10 8x
y 5 4x
1
11 1
x
57. y 3
12 6
5y 9 2x
y
y
9 2
x
5 5
58. xy x 2
3y 27x
5
60. A 1
3
3
7
2
2
3
4
det A 140 27 4 42 30 12 231
17 3 2
6
7 3
13
2
4
x
231
1
7
5
87180140 12675232 52
4
13
13
2, 3, 4
62. 13 3i
63. 6
64. 5 2i
65. 6 5i
66. 6 48i
67. 14 15 6i 35i 29 29i
68.
1
3i 3i
3i 3i
10
69.
4 3i 9 2i 36 6 27i 8i 30 35i
85
9 2i 9 2i
81 4
476 117 24 182 102 72
231
231
1
231
5 17 2
1
6 3
3 13
4
y
231
y 9x
2
y 1
x
4
3
5
75 294 58 45 203 140 39
3
13
13
1 4 14
2
3 15
3
5 29
z
13
11 1
x
4
2
59. x 3y 28x
xy 2 x
1
2
3
210 812 75 87 490 300 26
2
13
13
1 14
1
2 15
7
3 29 5
y
13
55. 8x 2y 10
56. 2x 5y 9
455 54 34 357 60 39 693
3
231
231
y x 2 4x 5
y 1 3x
det A 15 84 10 9 35 40 13
14 4
1
15
3
7
29
5 5
x
13
x
54. 3x y 1
3 17
7
6
2 13
231
1, 2, 3
y
y
5
1
3
7i
6
17 17
Lesson 5.8
Activity (p. 307)
1. a b c 2; 9a 3b c 0
120 153 26 36 195 68 462
2
231
231
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Algebra 2
Chapter 5 Worked-out Solution Key
153
Chapter 5 continued
1
3
2
1
2. A 9
4
6. 100a 10b c 165
1
1
1
36a 6b c 115
det A 3 4
2 1
0
3
0 2
a
20
1
2
9
0
4
0
b
20
1 1
9
3
4 2
c
20
18 12 2 9 20
1
1
1
64
1
20
2
1
1
1
8 18 10 1
20
20 2
2
0
0
36 24 60
3
20
20
21, 21, 3; y 12x
2
y
5.8 Practice and Applications (pp. 309–312)
7. y ax 22 2
2 a22 2
4 4a
y x 22 2
1
1
1
4. 4 a0 10 2
13.
b
c
16
1
4
2
2
4
30
1
1
1
90
3
30
16
1
4
4
1
2
30
3 4a
4 4a
34
1a
a
y x 22 1
12.
y ax 42 5
9 a1 42 6
3 a8 42 5
3 9a
8 16a
1
3
12 a
a
y ax 2
y 12x 42 5
y ax 12 10
14.
12 4a
54 a3 12 10
3 a
54 a16 10
y 3x 2
30
1
30
3 a4 22 1
y 13x 42 6
2. 2; 3
det A 16 16 2 4 32 4 30
2 4
1
2
1
1
4 2
1
2 16 4 4 4 8
a
30
30
3 a1 1
11. y ax 4 6
y 2x 1x 2
4
1
2
10. y ax 22 1
2
2a
16
1
4
y 2x 12 4
y ax 12
9.
5.8 Guided Practice (p. 309)
5. A 2 a
1a
3
3. y x 12 3
y ax 12 4
2 a2 12 4
2
6
1. best-fitting quadratic model
8.
y 34x 12
1
y
p 1.83t2 19.55t 172.73
1
x3
2
3. y 2 x 2x 3
12x2 x
1
1
2x2 2x
16a 4b c 154.5
64 16a
4a
y 4x 12 10
15.
y ax 62 7
y ax 3x 3
61 36a 7
4 a1 31 3
54 36a
4 a24
32
a
y 32x 62 7
17.
16.
1
2
a
y 12x 3x 3
y ax 2x 1
6 a1 21 1
6 2a
32 8 4 8 64 2
30
2
2
4
64 32 4 8 64 16 60
2
30
30
3a
y 3x 2x 1
18.
y ax 0x 4
3 a31
1 a
y x 0x 4
19. y ax 1x 4
2 a3 13 4
2 a21
1 a
y x 1x 4
y x2 3x 2
154
Algebra 2
Chapter 5 Worked-out Solution Key
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Chapter 5 continued
20. y ax 2x 2
21.
y ax 1x 6
8 a4 24 2
20 a1 11 6
8 a26
20 a25
2
3
a
y
2x 2
y ax 10x 8
22.
9a 3b c 4
36a 6b c 8
y x2 5x 2
2a
2
3 x
abc2
29.
y 2x 1x 6
30. 4a 2b c 1
a b c 11
15 a7 107 8
4a 2b c 27
15 a31
y 3x2 7x 1
5 a
y 5x 10x 8
23.
y ax 3x 9
31. 16a 4b c 7
77 a14 314 9
9a 3b c 3
77 a115
9a 3b c 21
7
5
y 2x2 4x 9
a
y 75x 3x 9
24.
y ax 0x 5
32.
9a 3b c 4
abc0
18 a3 03 5
81a 9b c 10
18 a32
y 0.25x2 x 1.25
3 a
y 3x 0x 5
25.
abc2
c4
33. 36a 6b c 46
4a 2b c 14
9a 3b c 2
16a 4b c 56
y x x 4
2
y 2.5x2 6x 8
26.
4a 2b c 7
9a 3b c 2
34.
h as 272 16
25a 5b c 4
40 a20 272 16
y 2x2 15x 29
24 a49
24
49
2
h 24
49 s 27 16
27. 25a 5b c 4
16a 4b c 0
c1
y 0.75x2 2.75x 1
a
35.
y ax 0x 24
0.2 a1717 24
0.2 119a
0.00168 a
28.
abc5
y 0.00168x 0x 24
c3
9a 3b c 9
y x2 x 3
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Algebra 2
Chapter 5 Worked-out Solution Key
155
Chapter 5 continued
36. 66a 4b c 1.42
b. 100a 10b c 58.3
4a 2b c 0.57
900a 30b c 126.9
36a 6b c 1.42
2304a 48b c 139.3
t
d 0.0738A2 6.4304A 0.6928
0.3086s 0.005
Change in finishing
time (seconds)
Distance (meters)
0.0119s2
160
140
120
100
80
60
40
20
0
0
Wind speed
(meters per second)
37. a.
38,025a 195b c 8130
900a 30b c 122.8
160,801a 401b c 9810
2304a 48b c 137.8
Shoulder weight (grams)
s 0.0807f 2 55.229f 330.38
keep increasing as the diameter increases.
b. 0.0675, 0.0672, 0.0678, 0.0678, 0.0681, 0.0681, 0.068;
the ratios are approximately equal.
c. t 0.068d2; about 206 min
b. 57,121a 239b c 8130
111,556a 334b c 9690
139,129a 373b c 8990
k 0.1422f 2 97.015f 6926.7
Kidney weight (grams)
d 0.07A2 6.2284A 0.2623
39. a. 1.35, 1.68, 2.03, 2.37, 2.725, 3.07, 3.4; no, the ratios
12000
10000
8000
6000
4000
2000
0
0 100 200 300 400 500
Protein intake (grams per day)
40.
n
0
1
2
3
4
5
6
R
1
2
4
7
11
16
22
abc2
9a 3b c 7
25a 5b c 16
R 0.5N 2 0.5N 1
600
500
400
300
200
100
0
5.8 Mixed Review (p. 312)
41. 32 4 9 4 5
42. 25 2
0 100 200 300 400 500
Protein intake (grams per day)
38. a. 100a 10b c 61.2
900a 30b c 130.4
2304a 48b c 140.7
d 0.0771A2 6.5803A 2.4614
Distance (meters)
80
c. 100a 10b c 56.1
88,209a 297b c 9680
160
140
120
100
80
60
40
20
0
2 2 2 2 32
43. 34 10 364 10 192 10 182
3
44. 14 21 7 1 2 7 4
45. x y 4
xy2
46.
2x y 0
5x 3y 11
2x 6
5x 32x 11
x3
5x 6x 11
3y4
11x 11
1 y
3, 1
x1
y 21
y2
0 10 20 30 40 50 60 70
Angle (degrees)
156
20
40
60
Angle (degrees)
Algebra 2
Chapter 5 Worked-out Solution Key
1, 2
Copyright © McDougal Littell Inc.
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Chapter 5 continued
47. 3x 2y 2
6.
4x 7y 19
y
y x 2 7x 10
3x
4x 7 1 19
2
1
1
21x
4x 7 19
2
y x 2 4x
13
x 26
2
7. y ax 52 2
x 4
3 4
2
y 1 5 a51
2a
1 a
y 2x 5 2
y x 3x 1
9. 16a 4b c 8
4, 5
16a 4b c 8
4a 2b c 1
48. C 1800 15v 10p
8a 4b 2c 10
4a 2b c 5
Quiz 3 (p. 312)
y ax 3x 1
8.
0 a12 2
2
y 1 6 5
1.
1 x
3c 18
24a
Eq 2
4a 2b c 1
y
4a 2b c 5
8a 2c 6 Eq 1
y x2 2
1
1
1
x
1
8a 2c 6
8a 6
8a c 6
a4
3
c0
2.
y
434 2b 0 5
y x 2 x 3
2b 2
1
b1
1
1
x
1
y
3 2
4x
x
10. 0.00339N2 0.00143N 5.95 < 1000
3.
4.
y
0.00339N2 0.42N 0.0441 < 1005.95 0.0001495
y
y x2
0.00339N 0.212 < 1005.9502
1
1
1
N 0.212 < 296,740
1
x
1
N 0.21 < 544.7
x
1
1
1 y 2x 2 1
N < 544
y 2x 2 12x 15
0 < N < 544
5.
y
Chapter 5 Review (pp. 314–316)
y x 2 2x 3
1.
1
y
x
1
y x 2 2x 3
y x 2 4x 7
(2, 3)
1
x 2
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1
1
1 x
Algebra 2
Chapter 5 Worked-out Solution Key
157
Chapter 5 continued
2.
x2 4x 3
18.
x2
y
x2
(2, 5)
x2 10x 26
19.
4x 4 7
x2
10x 25 1
x 2 7
x 52 1
2
x 2 ± 7
y 3(x 2)2 5
1
x
1
x 5 ±i
x5 ± i
x 2 ± 7
20.
2w2
w70
1
1
7
1
w2 w 2
16 2 16
3.
y
w 41
1
1
x
1
w
2
57
16
57
1
±
4
4
1
y 2 (x 1)(x 5)
w
(2, 4.5)
x2
1 57
±
4
4
y x2 8x 17
21.
4. x2 11x 24 0
y 17 16 x2 8x 16
x 3x 8 0
y x 42 1;
4, 1
x 3 or x 8
5. x2 8x 16 0
7.
2x2 3x 1 0
6.
x 42 0
2x 1x 1 0
x4
x 12 or x 1
3u2 4u 15 0
8. 25v2 30v 9 0
u 33u 5 0
5v 32 0
u 3 or u 5
3
9. 2x2 200
v
10. 5x2 15
x2 100
3
5
y x2 2x 6
22.
y 6 x2 2x
y x2 2x 1 5
y x 12 5;
1, 5
y 4x2 16x 23
23.
y 23 4x2 4x
y 4x2 4x 4 7
x2 3
y 4x 22 7;
x ± 3
x ± 10
11. 4t 62 160
t 62 40
t 6 ± 210
2, 7
24. x2 8x 5 0
x
8 ± 64 20
2
x
7 ± 49 36
18
x
8 ± 44
2
x
7 ± 85
18
t ± 210 6
2
12. k 1 7 43
k 12 50
k 12 50
k 1 ± 52
k 1 ± 52
13. 7 2 4i 5i 5 i
14. 2 6 11i i 4 12i
15. 12 90 40i 27i 102 13i
16.
8i
1 2i 8 2 i 16i 6 17i
1 2i 1 2i
14
5
25. 9x2 7x 1 0
x 4 ± 11
26. 4v2 10v 7 0
v
10 ± 100 112
8
v
10 ± 2i3
8
v
5 ± i3
4
17. 62 92 36 81 117 313
158
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
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Chapter 5 continued
2.
y
27.
y
y x 2 4x 4
1
1
1
y (x 3)2 1
x
1
1
(3, 1)
x
1
1
x 3
28.
29.
y
y
1
y 2x 2 3
3.
1
(2, 3) y 3 (x 1)(x 5)
1
1
y x 2 6x 5
x2
30.
x2
y
1 x
1
1
x
3x 4 ≤ 0
x
1
1
x 4x 1 0
x 4 or x 1
y 7 4x2 6x 9
1 ≤ x ≤ 4
y 7 4x2 24x 36
31. 2x2 7x 2 ≥ 0
x
7 ± 49 16
4
y 4x2 24x 29
5. x2 x 20 x 5x 4
7 ± 33
x
4
6. 9x2 6x 1 3x 12
7 33
7 33
or x ≥
x ≤
4
4
5 a4 62 1
x2 49
9
7
3
x < 73 or x >
4 4a
7
3
8. y x2 10x 16
y x 8x 2;
8, 2
9. a. 5
a1
y x 62 1
34.
7. 3u2 108 3u2 36 3u 6u 6
33. y ax 62 1
32. 9x2 > 49
x ±
y 4x 32 7
4.
y ax 4x 3
35.
25a 5b c 1
20 a1 41 3
16a 4b c 2
20 a10
9a 3b c 5
2 a
b.
5 5 2 2 105
83 83
33
10.
26
3
11. 3 1 i 5i
imaginary
4 4i
4 + 2i
5 i
y 0.5x2 1.5x 4
i
1
i
y 2x 4x 3
1
real
3i
Chapter 5 Test (p. 317)
1.
y
x2
12. 4 7 2i 3i 11 5i
(2, 3)
13. 48 2 6i 16i 46 22i
y 2x 2 8x 5
1
1
Copyright © McDougal Littell Inc.
All rights reserved.
x
14.
9 2i 1 4i 9 8 2i 36i 1 38i
1 4i 1 4i
1 16
17
Algebra 2
Chapter 5 Worked-out Solution Key
159
Chapter 5 continued
15. f z z2 0.5i
28.
y x 2 4x 2
y
29.
y
z0 0
1
z1 f 0 0.5i
z2 f 0.5i 0.25 0.5i
z3 f 0.25 0.5i 0.1875 0.5i
1
z0 0
z1 0.5
z2 0.0625 .25 0.3125 0.56
z3 0.18752 0.52 0.53
x
x 22
18. c 0.09;
x 0.32
x2 x 6 0
2x2 32
x 3x 2 0
x2 16
x ±4
2 ≤ x ≤ 3
121
4 ;
2
11
2
y x2 18x 4
19.
31. 2x 2 9 > 23
x 3 or x 2
17. c 1 x
y 2x 2 12x 15
x
1
x2 x 6 ≥ 0
30.
Yes, the absolute values are less than N 1.
16. c 4;
1
1
2
x < 4 or x > 4
7 ± 49 16
32. x 2
x
y 4 81 x2 18x 81
y x 92 85;
7 ± 33
2
7 33
7 33
< x <
2
2
9, 85
y ax 32 2
y ax 1x 8
20. 7x2 3 11
21. 5x2 60x 180 0
7x2 14
x2 12x 36 0
18 a1 32 2
2 a2 12 8
x2 2
x 6x 6 0
20 4a
2 a6
x ± 2
4x2
22.
23.
2x 152x 1 0
x
or x m2
8 ± 64 12
2
m 4 ±
52
p 9 27
p 9 ± 33
26. 12 4710
t
3 ± i7
4
27.
16a 4b c 2
167 16t2
167
16
t 3.23
37. p 1.225a2 88a 1697.375
Chapter 5 Standardized Test (pp. 318–319)
1. B
2. 4x2 4x 35 2x 52x 7
y
3. y 279;
x2
13x 40
0 x 5x 8
2 imaginary
1
E
4. 4x 12 28
x 12 7
x 1 ± 7
5, 8
yx21
1
1
t2
about 3.23 sec
3 ± 9 16
t
4
p 9 ± 33
0 16t2 167
36.
y x2 8x 14
25. 2t2 3t 2 0
2
abc7
35.
a
y 13x 1x 8
2
25a 5b c 1
2
m 4 ± 13
24. 3p 92 81
1
3
y 5x 3 2
8m 3 0
m
1
2
34.
5 a
x6
28 15 0
15
2
33.
x 1 ± 7
D
x
C
5. 12 8i10 i 120 8 80i 12i
112 92i
D
6. C
160
Algebra 2
Chapter 5 Worked-out Solution Key
Copyright © McDougal Littell Inc.
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Chapter 5 continued
7. 22 437 88
8. x2 7x 8 > 0
2 real solutions
x2 7x 8 0
A
x 8x 1 0
x 8 or x 1
x < 8 or x > 1
B
9. D
10. E
11. 32 22 9 4 13 3.61 or
12 42 1 17 18 32 4.24 B
12. 49 96 145 or 196 200 4
13. a. r 0.334302
A
400 0.334s2
b.
1197.6 s2
r 300.6 ft
34.6 s
about 34.6 mih
c. A 24r
14. a. h d. A 8.016s2
16t2
e. linear; quadratic
40t 3
b. h 3 16t2 40t
h 3 16t2 2.5t 1.5625
h 3 16t 1.252
h 16t 1.252 3 25
h 16t 1.252 28
about 1.25 sec
8 16t 1.252 28
c.
20
t 1.252
16
5
t 1.252
4
±
1.25
5
2
5
t 1.25
2
t
about 2.37 sec
6 ≤ 16t 1.252 28 ≤ 9
d.
22
19
≥ t 1.252 ≥
16
16
1.375 ≥ t 1.252 ≥ 1.1875
1.173 ≥ t 1.25 ≥ 1.090
2.42 ≥ t ≥ 2.34
from about 2.34 sec to 2.42 sec
e.
0 160.12 0.1v0 8
0 0.16 8 0.1v0
7.84 0.1v0
78.4 v0
78.4 feet per sec
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Algebra 2
Chapter 5 Worked-out Solution Key
161