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

13.
f x x 2 5 14.
Vertex:
Axis of symmetry: x 0 or the y-axis
Find x-intercepts:
x 2 5 0
x 2 5
0, 5
x ±5
x-intercepts:
5, 0, 5, 0
1
2 x2 4 0
x 2 8
x-intercepts:
x ±8 ±22
22, 0, 22, 0
2
1
−4 −3 −1 1 3 4
−2
−3
−6
y
3
2
1
−4 −3 −1 1 2 3 4
−2
−3
−5
x
x
Section 2.1 Quadratic Functions and Models 139
hx 25 x 2
Vertex:
0, 25
Axis of symmetry:
Find x-intercepts:
25 x 2 0
x 2 25
x ±5
x-intercepts: ±5, 0
16 1
4 x2 0
x 2 64
x ±8
x-intercepts: ±8, 0
x 0
15. f x
Vertex: 0, 4
Axis of symmetry: x 0 or the y-axis
Find x-intercepts:
y
1
2x2 4 1
2x 02 4 16.
Vertex: 0, 16
Axis of symmetry: x 0
Find x-intercepts:
17.
19.
f x x 5 y
2 6 18.
Vertex:
5, 6
Axis of symmetry:
Find x-intercepts:
x 5 2 6 0
x 5 2 6
x 5 ±6
x 5
x 5 ± 6
x-intercepts: 5 6, 0, 5 6, 0
20
16
12
−20 −12 4 8
−8
x
f x 16 1
4 x2 1
4 x2 16
f x x 6 2 3
Vertex:
6, 3
Axis of symmetry:
Find x-intercepts:
x 6 2 3 0
x 6 2 3
Not possible for real x
No x-intercepts
x 6
hx x2 8x 16 x 42 20. gx x2 2x 1 x 12 Vertex:
4, 0
Axis of symmetry: x 4
x-intercept: 4, 0
20
16
12
8
4
y
−4 4 8 12 16
x
Vertex:
1, 0
Axis of symmetry: x 1
x-intercept: 1, 0
30
−20 −10
10 20
y
18
12
9
6
3
y
−9 −6 −3
−3
50
40
30
20
10
y
3 6 9
−20 −10 10 20 30
−4 −3 −2 −1 1 2
6
5
4
3
2
1
y
x
x
x
x