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

9.
11.
13.
hx 4x2 4x 13 10. f x x2 6x 1
Vertex:
4x 2 x 13
4x2 x 1 1
13
4 4
4x2 x 1
1 13
4
1
4x 2 2
12
1, 12 2
Axis of symmetry:
1
x 2 2
1
0 4x 2
3
2
12
No real zeros
x-intercepts: none
hx x 2 5x 4
x 2 5x 25
4
x 1
2
5
x 2 2
25 16
4 4
Vertex: 5 5
x 2
, 41
2 2
41
4
Axis of symmetry:
0 x 2 5x 4
4
By the Quadratic Formula, x
5 ± 41
x-intercepts: , 0 2
fx 1
3 x2 5x 4
Vertex:
25
4
x 5
2
4
20
15
10
5
−3 −2 −1 1 2 3
−8
1 5
x 3 2 2
41
4
1
3x2 5x 25 25
4
4 4
1 5
x 3 2 2
41
12
5, 41
2 12
Axis of symmetry: x 5
2
−6
−4
y
5 ± 41
.
2
−2 2
−2
−4
−10
y
0 x 2 5x 4
x
x
12.
−8
Vertex: 3, 8
Axis of symmetry:
0 x 2 6x 1
x 3 2 8
6 ± 32
2
x-intercepts: 3 ± 22, 0
Review Exercises for Chapter 2 239
x 2 6x 9 9 1
x 3
x 6 ± 62 411
21
Vertex:
1, 4 2
x- intercepts: None
3 ± 22
fx 4x 2 4x 5
1
4x 2 2
4
2
−2
−2
4x2 x 1 1 5
4 4 4
1
4x 2 2
1
−4
−6
−8
Axis of symmetry:
0 4x
4 ± 8i
By the Quadratic Formula, x
8
The equation has no real zeros.
2 4x 5
x 1
2
−8 −6 −4
−6
−4
By the Quadratic Formula, x
5 ± 41
x-intercepts: , 0 2
4
2
−2 2
−4
−6
y
5 ± 41
.
2
x
y
2
4 8
12
10
8
2
−2
−2
y
10
2 4 6
1
± i.
2
x
x