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

25.
27.
29.
hx 4x 2 4x 21
Vertex:
Vertex:
4x2 x 1 1
4 4 21 4
1
4x 2 2
20
1
, 20 2
Axis of symmetry:
Find x-intercepts:
4x 2 4x 21 0
x
f x 1
4 x2 2x 12
1
4x 2 8x 16 1
416 12
1
4x 4 2 16
4, 16
Axis of symmetry:
Find x-intercepts:
1
4 x2 2x 12 0
x 2 8x 48 0
x 4x 12 0
x 4 or x 12
x 1
2
4 ± 16 336
24
Not a real number ⇒ No x-intercepts
x 4
x-intercepts: 4, 0, 12, 0
−8 −4
4 8
−8
4
−12
−16
−20
y
4 8 16
f x x 2 2x 3 x 1 2 4 30.
Vertex:
1, 4
Axis of symmetry: x 1
x-intercepts: 3, 0, 1, 0
20
10
y
−8 7
5
−5
x
x
Section 2.1 Quadratic Functions and Models 141
26.
28.
2x2 1
f x 2x
x 1
2 2 x 1
Vertex:
1
2x 4 2
2 1
1
16
1
2x 4 2
7
8
1 7
,
4 8
Axis of symmetry:
Find x- intercepts:
2 x 2 x 1 0
x
Not a real number
No x-intercepts
Vertex:
Axis of symmetry:
Find x-intercepts:
1
3 x2 3x 6 0
x 2 9x 18 0
x 3x 6 0
x 1
4
1 ± 1 8
22
f x 1
3x 2 3x 6
1
3x 2 9x 6
1
3x2 9x 81
4 1
381 4 6
1
3x 9
9 3
2 , 4
2 2
3
4
x 9
2
x-intercepts: 3, 0, 6, 0
f x x 2 x 30
x 2 x 30
6
5
4
3
1
−3 −2 −1 1 2 3
2
−2
−2
−4
−6
x2 x 1
4 1
4 30
x 1
2 2 121
4
Vertex:
Axis of symmetry: x
x-intercepts: 6, 0, 5, 0
1
2
y
y
4 6
8 10
1
2, 121
4 −10 10
35
−80
x
x