Prerequisite Skills (p. 234) x y 1 1 5 25(23)

Chapter 4
Prerequisite Skills (p. 234)
Lesson 4.1
1. The x-intercept of the line shown is 3.
4.1 Guided Practice (pp. 237–239)
2. The y-intercept of the line shown is 2.
1. y 5 24x2
3. 25x 1 1 5 25(23) 1 1
2
2
5 25(9) 1 1
5 245 1 1
x
22
21
0
1
2
y
216
24
0
24
216
5 244
Both graphs have the same
vertex and axis of symmetry.
However, the graph of
y 5 24x2 opens down and is
narrower than the graph of
y 5 x2 .
y
4. x 2 x 2 8 5 (23) 2 (23) 2 8
2
2
y 5 x2
2
5 9 2 (23) 2 8
x
1
591328
y 5 24x 2
54
5. (x 1 4)2 5 (23 1 4)2 5 (1)2 5 1
6. 23(x 2 7)2 1 2 5 23(23 2 7)2 1 2
5 23(210)2 1 2
5 23(100) 1 2
2. y 5 2x 2 2 5
5 2300 1 2
5 2298
7.
8.
y
y
x
22
21
0
1
2
y
29
26
25
26
29
y
1
21
21
(3, 0)
x
x
y
9.
x
1
1
(0, 2)
Both graphs have the same
axis of symmetry. However,
the graph of y 5 2x 2 2 5
opens down, and its vertex is
5 units lower.
y 5 x2
1
1
y 5 2x 2 2 5
y
10.
(0, 0)
21
x
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
(5, 4)
1
21
11. x 1 8 5 0
x 5 28
x
12. 3x 2 5 5 0
3x 5 5
5
1
3. f(x) 5 } x 2 1 2
4
x
24
22
0
2
4
y
6
3
2
3
6
x 5 }3
13. 2x 1 1 5 x
14. 4(x 2 3) 5 x 1 9
x1150
4x 2 12 5 x 1 9
Both graphs open up and have
the same axis of symmetry.
However, the graph of
3x 2 12 5 9
f (x) 5 }4 x2 1 2 is
x 5 21
f(x)
1
3x 5 21
x57
f(x) 5
1
1
f(x) 5 4 x 2 1 2
wider than the graph of
f (x) 5 x2, and its vertex is
2 units higher.
x2
1
x
4. y 5 x 2 2 2x 2 1
y x51
(22)
b
x 5 2}
5 2}
51
2a
2(1)
y 5 (1) 2 2(1) 2 1 5 22
2
Vertex: (1,22)
Axis of symmetry: x 5 1
1
21
x
(1, 22)
y-intercept: 21; (0, 21)
x 5 21: y 5 (21)2 2 2(21) 2 1 5 2; (21, 2)
Algebra 2
Worked-Out Solution Key
173
Chapter 4,
continued
5. y 5 2x 2 1 6x 1 3
3
3
x 5 2}
5 2}
5 2}2
2a
2(2)
y 5 21 2}2 2 1 61 2}2 2 1 3
3 2
3
23
3
2
3
2
(2 , 2 )
3
2
5 2}
x5
1
3
3
Vertex: 2}2 , 2}2
x
3
22
2
x
22
y
16
x
22
21 0
y
212
23 0 23
x
24
x 5 21: y 5 2(21) 1 6(21) 1 3 5 21; (21, 21)
y
8
2
15 83
, 4
2
(2
(25)
y
)
15
21 2}3 2
y 5 2}31 2}
2 51 2}
12
22
22
15 2
15
83
15
x 5 22
22
x
Vertex: 1 2}
,}
2 42
15 83
15
2
Axis of symmetry: x 5 2}
y-intercept: 2; (0, 2)
1
x 5 23: y 5 2}3 (23) 2 2 5(23) 1 2 5 14; (23, 14)
7. y 5 4x 2 1 16x 2 3
16
b
2
212
22 0 2 4
2
0 2 8
x
26
23 0
3
6
y
212
23 0
23
212
7. y 5 3x 2
3
5}
4
1
1
6. y 5 2}x 2
3
x 5 2}
5 2}
5 2}
2a
2
1
1
0 4 16
4. y 5 23x 2
y-intercept: 3; (0, 3)
b
4
2
1
5. y 5 }x2
2
3
Axis of symmetry: x 5 2}2
1
6. f (x) 5 2}x 2 2 5x 1 2
3
21 0 1
x 5 2}
5 2}
5 22
2a
2(4)
y 5 4(22)2 1 16(22) 2 3 5 219
The minimum value is y 5 219.
8. R(x) 5 (35 2 x) + (380 1 40x)
R(x) 5 13,300 1 1400x 2 380x 2 40x 2
R(x) 5 240x 1 1020x 1 13,300
x
22
y
12
21 0 1
3
y
2
0 3 12
Both graphs open up and have
the same vertex and axis of
symmetry. However, the graph
of y 5 3x 2 is narrower than
the graph of y 5 x 2.
8. y 5 5x
y 5 3x 2
2
y 5 x2
x
22
y
20
21 0 1
5
y
2
0 5 20
Both graphs open up and have
the same vertex and axis of
symmetry. However, the graph
of y 5 5x 2 is narrower than the
graph of y 5 x 2.
4
y 5 5x 2
y 5 x2
2
1020
b
x5}
5 2}
5 12.75
2a
2(240)
R(12.75) 5 240(12.75) 1 1020(12.75) 1 13,300
The vertex is (12.75, 19,802.5), which means the owner
should reduce the price per racer by $12.75 to increase
the weekly revenue to $19,802.50.
4.1 Exercises (pp. 240–243)
Skill Practice
1. The graph of a quadratic function is called a parabola.
2. Look at the value of a in the quadratic function. If a > 0,
the function has a minimum value. If a < 0, the function
has a maximum value.
174
Algebra 2
Worked-Out Solution Key
x
1
9. y 5 22x 2
x
2
5 19,802.5
x
1
2
y
22
28
21 0
1
22 0 22
y
2
28
Both graphs have the same
vertex and axis of symmetry.
However, the graph of
y 5 22x 2 opens down and is
narrower than the graph
of y 5 x 2.
y 5 x2
1
1
x
y 5 22x 2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
6
b
3. y 5 4x 2
y
Chapter 4,
continued
10. y 5 2x 2
15. f (x) 5 2x 2 1 2
x
22
21 0
y
24
21 0 21
1
y
2
24
y 5 x2
1
Both graphs have the same
vertex and axis of symmetry.
However, the graph of y 5 2x 2
opens down.
26
23
0
3
x
1
y 5 2x 2
f (x)
12
3
0
3 12
Both graphs open up and have
the same vertex and axis of
symmetry. However, the graph
1
3
f (x)
22
21 0
1
2
1
2
1
22
x
22
21
0
g (x)
213
27
25
g(x) 5
x2
x
1
x
graph of f(x) 5 x .
1
12. g(x) 5 2}x 2
4
22
0
g (x)
24
21
0 21
2
g(x)
g(x) 5
1
x
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
24
x
f (x)
22
0
2
4
7
22
25
22
7
graph of f (x) 5 }4 x 2 2 5 is
2
21
21 0
6
1
1
2
6
21
Both graphs open up and have
the same axis of symmetry.
However, the graph of
y 5 5x 2 1 1 is narrower than
the graph of y 5 x 2 and its
vertex is 1 unit higher.
y
3
f(x) 5 4 x 2 2 5
1
18. g(x) 5 2 } x 2 2 2
5
6
y 5 x2
y5
5x2 1
22
y
17
210
25
0
g (x)
222
27
22
1
1
2
5
17
Both graphs open up and have
the same axis of symmetry.
However, the graph of
y 5 4x 2 1 1 is narrower than
the graph of y 5 x 2 and its
vertex is 1 unit higher.
g(x) 5 2 5 x 2 2 2
y
5
6
3
10
27 222
y
g(x) 5 x 2
1
21 0
5
x
x
1
1
14. y 5 4x 2 1 1
x
wider than the graph of
f(x) 5 x 2 and its vertex is
5 units lower.
x
1
13. y 5 5x 2 1 1
y
Both graphs open up and
have the same axis of
symmetry. However, the
3
1
g(x) 5 2 4 x 2
22
2
24
f(x) 5 x 2 f(x)
is wider than the graph of
g(x) 5 x2.
x
x
3
17. f (x) 5 } x 2 2 5
4
1
g(x) 5 2}4 x 2 opens down and
2
1
4
Both graphs have the same
vertex and axis of symmetry.
However, the graph of
x2
12
Both graphs have the
same axis of symmetry.
However, the graph of
g(x) 5 22x 2 2 5 opens
down and is narrower than
the graph of g(x) 5 x 2. Also,
its vertex is 5 units lower.
g(x) 5 22x 2 2 5
24
2x 2
27 213
2
2
2
x
f(x) 5
1
g(x)
f(x) 5 x 2
of f (x) 5 } x 2 is wider than the
f(x) 5 x 2
Both graphs have the same axis
of symmetry. However, the
graph of f(x) 5 2x 2 1 2
opens down and its vertex is
2 units higher.
4
1
f(x) 5 3 x 2
f(x)
16. g(x) 5 22x 2 2 5
f(x)
6
22
1
1
11. f (x) 5 }x 2
3
x
x
x
Both graphs have the
same axis of symmetry.
However, the graph of
1
g(x) 5 2 }5 x 2 2 2 opens
down and is wider than the
graph of g(x) 5 x 2. Also,
its vertex is 2 units lower.
4
y5
y 5 4x2 1 1
1
x2
x
b
19. The x-coordinate of the vertex of a parabola is 2},
2a
b
not }
. The x-coordinate of the vertex is:
2a
24
b
x52}
5 2}
5 23.
2(4)
2a
Algebra 2
Worked-Out Solution Key
175
Chapter 4,
continued
26. f(x) 5 26x 2 2 4x 2 5
20. It is correct that the y-intercept of the graph is the value
of c. However, the value of c in y 5 4x 1 24x 2 7
is 27.
2
21. y 5 x 2 1 2x 1 1
(21, 0)
x 5 21
Vertex: (21, 0)
1
x
Axis of symmetry: x 5 21
1
3
1
13
3
(2 , 2 )
1
3
Axis of symmetry: x 5 2}
x
x 5 1:
x 5 1: y 5 12 1 2(1) 1 1 5 4; (1, 4)
22. y 5 3x 2 2 6x 1 4
f(1) 5 26(1)2 2 4(1) 2 5
y
2
27. y 5 }x2 2 3x 1 6
3
(23)
9
b
x 5 2}
5 2}
5 }4
2a
2
21 } 2
y 5 3(1) 2 6(1) 1 4 5 1
2
Vertex: (1, 1)
2
Axis of symmetry: x 5 1
x
x51
x 5 21: y 5 3(21) 2 6(21) 1 4 5 13; (21, 13)
2
23. y 5 24x 2 1 8x 1 2
y
y 5 }31 }4 2 2 31 }4 2 1 6 5 }
8
2 9 2
21
9
9 21
4 8
(, )
3
23
Vertex: 1 }4, }
82
9 21
(1, 6)
8
x 5 2}
5 2}
51
2a
2(24)
y
3
(1, 1)
21
y-intercept: 4; (0, 4)
1
x 5 23
5 215; (1,215)
(26)
x 5 2}
5 2}
51
2a
2(3)
x5
x
9
4
9
Axis of symmetry: x 5 }4
2
y 5 24(1) 2 1 8(1) 1 2 5 6
21
x
Vertex: (1, 6)
y-intercept: 6; (0, 6)
2
x 5 23: y 5 }3 (23)2 2 3(23) 1 6 5 21; (23, 21)
y–intercept: 2; (0, 2)
x51
x 5 21: y 5 24(21) 1 8(21) 1 2 5 210; (21, 210)
2
24. y 5 22x 2 2 6x 1 3
(26)
3
(
3 15
2
22 ,
2
3
22
x
15
5}
2
1
2
8
21
13
x
5}
3
8 13
x 5 22
2
8
2
Vertex: 1 2}3, }
32
3
3 15
Vertex: 2}2 , }
2
13
3
y 5 2}41 2}3 2 2 41 2}3 2 2 1
3
y 5 221 2}2 2 2 61 2}2 2 1 3
8
3
(2 , )
8
21 2}4 2
x 5 2}
5 2}
5 2}2
2a
2(22)
3 2
(24)
b
y
8
x 5 23
x 5 2}
5 2}
5 2}3
2a
3
y
)
3
28. y 5 2}x 2 2 4x 2 1
4
8
Axis of symmetry: x 5 2}3
3
Axis of symmetry: x 5 2}2
y-intercept: 21; (0,21)
y-intercept: 3; (0, 3)
3
x 5 22: y 5 2}4(22)2 2 4(22) 2 1 5 4; (22, 4)
x 5 1: y 5 22(1) 2 6(1) 1 3 5 25; (1, 25)
2
25. g(x) 5 2x 2 2 2x 2 1
(22)
b
x 5 2}
5 2}
5 21
2a
2(21)
g(21) 5 2(21) 2 2 2(21) 2 1
(21, 0)
23
x 5 21
50
Vertex: (21, 0)
Axis of symmetry: x 5 21
y-intercept: 21; (0, 21)
x 5 1: g(1) 5 2(1) 2 2 2(1) 2 1 5 24; (1, 24)
Algebra 2
Worked-Out Solution Key
3
29. g(x) 5 2}x2 1 2x 1 2
5
y
1
x
y
5
3
g1 }3 2 5 2}51 }3 2 1 21 }3 2 1 2
5
3 5 2
11
5}
3
5
11
3
(, )
5
b
2
x 5 2}
5 2}
5 }3
2a
3
21 2}5 2
2
22
x
x5
5
3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Axis of symmetry: x 5 1
176
y
3
13
y-intercept: 25; (0,25)
y-intercept: 1; (0, 1)
b
13
1
Vertex: 1 2}3, 2}
32
1
y 5 (21) 1 2(21) 1 15 0
b
1 2
1
1
2
1
f 1 2}3 2 5 261 2}3 2 2 41 2}3 2 2 5 5 2}
3
y
b
2
x 5 2}
5 2}
5 21
2a
2(1)
b
(24)
b
x 5 2}
5 2}
5 2}3
2a
2(26)
Chapter 4,
continued
Vertex: 1 }3 , }
32
5 11
33. y 5 26x 2 2 1
Because a < 0, the function has a maximum value.
5
Axis of symmetry: x 5 }3
y-intercept: 2; (0, 2)
y 5 26(0)2 2 1 5 21
3
3
x 5 21: g(x) 5 2}5 (21)2 1 2(21) 1 2 5 2}5;
The maximum value is y 5 21.
34. y 5 9x2 1 7
1 21, 2}5 2
3
Because a > 0, the function has a minimum value.
b
0
b
1
30. f(x) 5 } x 2 1 x 2 3
2
x 5 21
5 2}
50
x 5 2}
2a
2(9)
y
y 5 9(0)2 1 7 5 7
1
1
x 5 2}
5 2}
5 21
2a
1
21 }2 2
1
f (21) 5 }2 (21)2 1 (21) 2 3
7
5 2}2
22
x
The minimum value is y 5 7.
35. f (x) 5 2x 2 1 8x 1 7
Because a > 0, the function has a minimum value.
7
2
(21, 2 )
8
b
x 5 2}
5 2}
5 22
2a
2(2)
Vertex: 1 21, 2}2 2
f (22) 5 2(22)2 1 8(22) 1 7 5 21
Axis of symmetry: x 5 21
The minimum value is f (x) 5 21.
7
36. g(x) 5 23x2 1 18x 2 5
y-intercept: 23; (0, 23)
Because a < 0, the function has a maximum value.
1
x 5 2: f (2) 5 }2 (2)2 1 2 2 3 5 1; (2, 1)
y
(24)
b
g(3) 5 23(3)2 1 18(3) 2 5 5 22
The maximum value is g(x) 5 22.
5
x 5 2}
5 2}
5 }4
2a
8
152
2}
3
37. f (x) 5 }x 2 1 6x 1 4
2
1
5 5
Vertex: }4 , }2
5
5
5
4
5
2
(, )
2
y 5 }5 1 }4 2 2 41 }4 2 1 5 5 }2
8 5 2
21
x5
2
Because a > 0, the function has a minimum value.
x
5
4
3
f (22) 5 }2 (22)2 1 6(22) 1 4 5 22
5
The minimum value is f (x) 5 22.
y-intercept: 5; (0, 5)
1
38. y 5 2} x 2 2 7x 1 2
4
x 5 21: y 5 }5 (21)2 2 4(21) 1 5 5 }
; 21, }
5 1
52
8
53
53
Because a < 0, the function has a maximum value.
5
32. y 5 2} x 2 2 x 2 4
3
y
1
(21)
3
b
x 5 2}
5 2}
5 2}
5
2a
10
}
21 23 2
2
1
b
21
x
2
3
,
10
(2
21 2}4 2
)
1
y 5 2}4 (214)2 2 7(214) 1 2 5 51
The maximum value is y 5 51.
39. D; Because the y-intercept changes from 2 to 23, the
77
5 2}
20
1
77
220
(27)
5 2}
5 214
x 5 2}
2a
1
3
x 5 210
5
3 2
3
y 5 2}3 2}
2 2}
24
10
10
3
77
Vertex: 2}
, 2}
10
20
6
b
5 2}
5 22
x 5 2}
2a
3
21 }2 2
Axis of symmetry: x 5 }4
1
18
b
5 2}
53
x 5 2}
2a
2(23)
8
31. y 5 } x 2 2 4x 1 5
5
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
0
b
5 2}
50
x 5 2}
2a
2(26)
vertex moves down the y-axis.
40. C; The graph of y 5 ax 2 1 bx 1 c is wider than the
2
graph of y 5 x2 if {a{ < 1.
41. y 5 20.02x 2 1 x 1 6
3
Axis of symmetry: x 5 2}
10
a 5 20.02
y-intercept: 24; (0, 24)
b51
1
5
20
20
; 1, 2}
x 5 1: y 5 2}3 (1)2 2 1 2 4 5 2}
3
3
2
c56
Algebra 2
Worked-Out Solution Key
177
Chapter 4,
continued
42. y 5 20.01x 2 1 0.7x 1 6
50. y 5 0.25x 2 2 1.5x 1 3
a 5 20.01
(21.5)
b
x 5 2}
5 2}
53
2a
2(0.25)
b 5 0.7
y 5 0.25(3)2 2 1.5(3) 1 3
c56
5 0.75
43. Vertex: (4, k)
b
x
Axis of symmetry: x 5 3
Sample answer: y 5 x2 2 8x 1 1
y-intercept: 3; (0, 3)
x 5 2: y 5 0.25(2)2 2 1.5(2) 1 3 5 1; (2, 1)
y 5 22x 1 16x 2 3
2
51.
1
y 5 2}2 x2 1 4x 1 5
f (x) 5 4.2x2 1 6x 2 11
b
x 5 2}
2a
44. C; y 5 0.5x2 2 2x
(22)
b
5 2}
52
x 5 2}
2a
2(0.5)
6
5
5 2}
5 2}7
2(4.2)
y 5 0.5(2)2 2 2(2) 5 22
f 1 2}7 2 5 4.21 2}7 22 1 61 2}7 2 2 1
5
Vertex: (2, 22)
5
45. A; y 5 0.5x 1 3
0
b
5 2}
50
x 5 2}
2a
2(0.5)
5
22
46. B; y 5 0.5x 2 2 2x 1 3
(22)
b
x 5 2}
5 2}
52
2a
2(0.5)
(
5
x 5 27
y
0
g(0) 5 1.75(0)2 2 2.5
x50
1
x50
x 5 2: g(2) 5 1.75(2)2 2 2.5 5 4.5; (2, 4.5)
21
x
5 4.5; (5, 4.5)
y
1
21
x
x50
g(0) 5 20.5(0)2 2 5 5 25
x
(0, 22.5)
Axis of symmetry: x 5 0
(0, 2)
2
22
Vertex: (0, 22.5)
Vertex: (0, 2)
Axis of symmetry: x 5 0
1
5 22.5
y
f (0) 5 0.1(0)2 1 2 5 2
53. Because the points (2, 3) and (24, 3) have the same
y-value and lie on the graph of a quadratic function, they
are mirror images of each other. The axis of symmetry
divides a parabola into mirror images, therefore, the axis
of symmetry is halfway between the x-values. The axis
of symmetry is x 5 21.
2 1 24
x5}
5 21
2
(0, 25)
54. y 5 ax2 1 bx 1 c
x 5 2: g(2) 5 20.5(2) 2 5
2
b
The x-coordinate of the vertex is 2}
.
2a
5 27; (2,27)
x 5 25
y 5 0.3(25) 1 3(25) 2 1
(25, 28.5)
Axis of symmetry: x 5 25
y-intercept: 21; (0, 21)
x 5 1: y 5 0.3(1)2 1 3(1) 2 1 5 2.3; (1, 2.3)
ab2
4a
a(b2 2 2b2)
2b2
1 b1 2}
1 c 5 }2 1 }
1c
y 5 a1 2}
2a 2
2a 2
2a
b 2
y
2
22
2
Vertex: (25, 28.5)
x
x 5 2}
5 2}
50
2a
2(1.75)
47. f (x) 5 0.1x 2 1 2
0
b
5 2}
50
x 5 2}
2a
2(0.1)
5 28.5
)
52. g(x) 5 1.75x 2 2 2.5
b
49. y 5 0.3x2 1 3x 2 1
3
b
x 5 2}
5 2}
5 25
2a
2(0.3)
1
22
27
x 5 1: f (1) 5 4.2(1)2 1 6(1) 2 1 5 9.2; (1, 9.2)
Vertex: (2, 1)
Axis of symmetry: x 5 0
5
27 ,
y-intercept: 21; (0, 21)
y 5 0.5(2)2 2 2(2) 1 3 5 1
Vertex: (0, 25)
2
5
Axis of symmetry: x 5 2}7
Vertex: (0, 3)
48. g(x) 5 20.5x 2 5
0
b
x 5 2}
5 2}
50
2a
2(20.5)
y
Vertex: 1 2}7, 2}
72
y 5 0.5(0)2 1 3 5 3
x 5 5: f (5) 5 0.1(5)2 1 2
5
22
5 2}
7
2
Algebra 2
Worked-Out Solution Key
(3, 0.75)
x
ab2 2 2ab2
4a
b
b2
1c5}
1 c 5 2}
1c
5}
2
2
4a
4a
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
b
1
21
Vertex: (3, 0.75)
2}
5 4 l 2}a 5 8
2a
178
x53
y
Chapter 4,
continued
Problem Solving
b.
55. R(x) 5 (1 1 0.05x) + (4000 2 80x)
0
x
R(x) 5 4000 2 80x 1 200x 2 4x2
120
b
3
4
x 5 2}
5 2}
5 15
2a
2(24)
x
R(15) 5 24(15)2 1 120(15) 1 4000 5 4900
P (x) 1562.5
Price: 1 1 0.05x l
c.
R(x)
Profits (dollars)
Price
Sales
5
+
(dollars/camera)
(cameras)
5
(320 2 20x)
2.5
1540
1520
0
1
2
3
4
x
Price decrease
R(x) 5 2100x2 1 200x 1 22,400
The theater should reduce the price per ticket by $2.50
to increase the weekly profit to $1562.50.
200
x 5 2}
5 2}
51
2a
2(2100)
g
60. y 5 2} x 2 1 x
10,000
R(1) 5 2100(1) 1 200(1) 1 22,400 5 22,500
2
32
a. ye 5 2} x 2 1 x 5 20.0032x 2 1 x
10,000
Price: 320 2 20x l
320 2 20(1) 5 300
5.3
x2 1 x 5 20.00053x2 1 x
ym 5 2}
10,000
The store should decrease the price per digital camera to
$300 to increase the monthly revenue to $22,500.
b.
ym 1 20.00053x2 1 x
7
1
57. y 5 } x2 2 } x 1 500
9000
15
b
7
1560
1500
0
+ (70 1 5x)
R(x) 5 22,400 1 1600x 2 1400x 2 100x2
b
6
(2.5, 1562.5)
The store should increase the price per song to $1.75 to
increase the daily revenue to $4900.
Revenue
(dollars)
5
P(x)
1580
1 1 0.05(15) 5 1.75
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
2
P (x) 1500 1540 1560 1560 1540 1500 1440 1360
R(x) 5 24x2 1 120x 1 4000
56.
1
7
1 2}
15 2
21 }
9000 2
x 5 2}
5 2}
5 2100
2a
1
7
1
(2100)2 2 }
(2100) 1 500 5 10
y5}
9000
15
ye 1 20.0032x2 1 x
The golf ball travels 312.5 feet on Earth.
The golf ball travels 1886.8 feet on the moon.
The height above the road of a cable at its lowest point
is 10 feet.
1886.8
c. A golf ball travels } or about 6 times further on
312.5
58. y 5 20.2x2 1 1.3x
b
1.3
the moon than on Earth. Smaller values of g produce
longer distances.
x 5 2}
5 2}
5 3.25
2a
2(20.2)
y 5 20.2(3.25)2 1 1.3(3.25) ø 2.1
P 5 2w 1 *
61.
No, the mouse cannot jump over a fence that is 3 feet
high because the maximum height it can jump is about
2.1 feet.
P 2 2w 5 *
A 5 *w 5 (P 2 2w)w 5 Pw 2 2w2 5 22w2 1 Pw
b
P
1
5 2}
5 }4P
w 5 2}
2a
2(22)
59. a.
Price
Profit
Sales
2 Expenses
5
+
(dollars/ticket)
(dollars)
(tickets)
(dollars)
A 5 221 }4P 2 1 P1 }4P 2 5 2}8 P 2 1 }4 P 2 5 }8 P 2
1
2
1
1
1
1
In terms of P, the maximum area that the swimming
P(x)
5
(20 2 x)
+ (150 1 10x) 2
5 3000 1 200x 2 150x 2 10x2 2 1500
5 210x2 1 50x 1 1500
1500
1
section can have is }8 P 2 ft2.
Mixed Review for TAKS
62. D;
Liz’s high score can be represented using the expression
3x 2 1200.
Algebra 2
Worked-Out Solution Key
179
Chapter 4,
continued
Lesson 4.2
63. G;
c 5 25n 1 1400
4.2 Guided Practice (pp. 246–248)
9900 5 25n 1 1400
1. y 5 (x 1 2)2 2 3
8500 5 25n
340 5 n
340 students attended the banquet.
Graphing Calculator Activity 4.1 (p. 244)
1. y 5 x 2 2 6x 1 4
The minimum value of the
function is y 5 25 and
occurs at x 5 3.
Minimum
X=3
Y=-5
2. f (x) 5 x 2 2 3x 1 3
The minimum value of the
function is f (x) 5 0.75 and
occurs at x 5 1.5.
Minimum
X=1
5
.
Y=0
5
7
.
3. y 5 23x 1 9x 1 2
2
The maximum value of the
function is y 5 8.75 and
occurs at x 5 1.5.
x 5 22
a 5 1, h 5 22, k 5 23
Vertex: (22, 23)
Axis of symmetry: x 5 22
x 5 0: y 5 (0 1 2)2 2 3
5 1; (0, 1)
(22, 23)
x 5 21: y 5 (21 1 2)2 2 3
5 22; (21, 22)
2. y 5 2(x 2 1)2 1 5
a 5 21, h 5 1, k 5 5
Vertex: (1, 5)
Axis of symmetry: x 5 1
1
x 5 0: y 5 2(0 2 1)2 1 5
22
5 4; (0, 4)
x 5 21: y 5 2(21 2 1)2 1 5 5 1; (21, 1)
1
3. f (x) 5 } (x 2 3)2 2 4
2
1
a 5 }2, h 5 3, k 5 24
Ma
imum
x
X=1
5
.
1
21
x
y (1, 5)
x
x51
x53
y
Vertex: (3,24)
Axis of symmetry: x 5 3
y
1
21
x
1
Y=8
5
7
.
x 5 1: f (x) 5 }2 (1 2 3)2 2 4
5 22; (1, 22)
4. y 5 0.5x 1 0.8x 2 2
2
(3, 24)
The minimum value of the
function is y 5 22.32 and
occurs at x 5 20.8.
4. The graphs of both functions open up and have the same
Minimium
X=-0
8
.
Y=-2
32
.
vertex and axis of symmetry. However, the a values of
the functions differ. The graph of the function
1
y5}
(x 2 1400)2 1 27 is wider than the graph of
7000
1
1
5. h(x) 5 } x 2 2 3x 1 2
2
(x 2 1400)2 1 27.
the function y 5 }
6500
The minimum value of the
function is h(x) 5 22.5 and
occurs at x 5 3.
5. y 5 (x 2 3)(x 2 7)
x-intercepts: p 5 3 and q 5 7
Minimium
X=3
Y=-2
5
.
p1q
x55
y
317
x5}
5}
55
2
2
1
1
x
(3, 0)
(7, 0)
y 5 (5 2 3)(5 2 7) 5 24
3
6. y 5 2} x 2 1 6x 2 5
8
Vertex: (5, 24)
The maximum value of the
function is y 5 19 and occurs
at x 5 8.
(5, 24)
Axis of symmetry: x 5 5
6. f (x) 5 2(x 2 4)(x 1 1)
Maximum
X=8
y
x-intercepts: p 5 4 and
Y=19
3
x52
2
q 5 21
22
4 1 (21)
p1q
3
5}
5 }2
x5}
2
2
x
(21, 0)
(4, 0)
f 1 }2 2 5 21 }2 2 4 21 }2 1 1 2
3
3
3
3
2
25
Vertex: 1 }2, 2}
22
3
25
3
Axis of symmetry: x 5 }2
180
Algebra 2
Worked-Out Solution Key
25
2
( ,2 )
5 2}
2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
1
x 5 21: f (x) 5 }2 (21 2 3)2 2 4 5 4; (21, 4)