C H A P T E R 2 Polynomial and Rational Functions

61.
fx 2x 10
2 7x 30 62.
x-intercepts:
0 2x 2 7x 30
5
2, 0, 6, 0
x or x 6
The x-intercepts and the solutions of f x 0 are the same.
5
0 2x 5)x 6
−40
2
fx 1
−5
10
Section 2.1 Quadratic Functions and Models 145
f x 4x 2 25x 21
x-intercepts:
7, 0, 3
4, 0
0 4x 2 25x 21
0 x 74x 3
x 7 0 ⇒ x 7
4x 3 0 ⇒ x 3
4
63.
2x 10
x-intercepts: 1, 0, 7, 0
2 6x 7 64.
x-intercepts: 15, 0, 3, 0
0 1
2x 2 6x 7
0 x 2 6x 7
0 x 1x 7
x 1
or
x 7
The x-intercepts and the solutions of f x 0 are the same.
x 1x 3
x 2 2x 3
gx x 1x 3
x 1x 3
x 2 2x 3
x 2 2x 3
−10
−6
opens downward
Note: f x ax 1x 3 has x-intercepts 1, 0
and 3, 0 for all real numbers a 0.
14
−9 2
The x-intercepts and the solutions of f x 0 are the same.
f x 7
10x 2 12x 45
0 7
10x 2 12x 45
0 x 15x 3
x 15 0 ⇒ x 15
x 3 0 ⇒ x 3
65. f x x 1x 3 opens upward
66. f x x 5x 5
x 2 10x
gx x 0x10
x 2 10x
opens downward
Note: f x ax 0x 10 axx 10 has
x-intercepts 0, 0 and 10, 0 for all real numbers
a 0.
The x-intercepts and the solutions of f x 0 are the same.
x 5x 5
x 2 25, opens upward
gx f x, opens downward
gx x 2 25
67. f x x 0x 10 opens upward
68. f x x 4x 8
f x x 3x 1
69. 22 opens upward
70.
x 3x 1
22
x 32x 1
2x 2 7x 3
gx 2x 2 7x 3
2x 2 7x 3
opens downward
Note: has x-intercepts
and for all real numbers a 0.
1
f x ax 32x 1
3, 0 2, 0
10
−70
10
−18 4
Note: f x ax has x-intercepts 5, 0 and
5, 0 for all real numbers a 0.
2 25
x 2 12x 32, opens upward
gx f x, opens downward
gx x 2 12x 32
Note: f x ax 4x 8 has x-intercepts 4, 0 and
8, 0 for all real numbers a 0.
f x 2x 5
2x 2
2x2 1
2x
2x 5
5
2x 2
2x 2 x 10, opens upward
gx f x, opens downward
gx 2x 2 x 10
5
f x ax
Note: 2x 2 has x-intercepts
and 2, 0 for all real numbers a 0.
−60
5
2 , 0