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

240 Chapter 2 Polynomial and Rational Functions
14.
f x 1
2 6x2 24x 22
3x 2 12x 11
3x 2 4x 4 4 11
3x 2 2 34 11
3x 2 2 1
Vertex: 2, 1
Axis of symmetry: x 2
0 3x 2 12x 11
x 12 ± 122 4311
23
3
x-intercepts: 2 ± , 0 3
15. Vertex:
Point:
Thus, fx 1
2x 4 2 1.
17. Vertex:
19. (a)
20.
Point:
2, 1 ⇒ 1 a2 4 2 1
2 4a
1
2 a
12 ± 12
6
14
12
10
8
6
4
2
y
–6 –4 –2 4 6 8 10
2 ± 3
3
4, 1 ⇒ fx ax 4 2 1 16. Vertex:
1, 4 ⇒ fx ax 1 2 4 18. Vertex:
2, 3 ⇒ 3 a2 1 2 4
1 a
Thus, fx x 1 2 4.
R 10p 2 800p
(a)
R20 $12,000
R25 $13,750
R30 $15,000
x
y
(b)
2x 2y 200
x y 100
Area xy
y 100 x
x100 x
100x x 2
x
2, 2 ⇒ fx ax 2 2 2
Point: 0, 3 ⇒ 3 a0 2 2 2
1 4a
1
4 a
fx 1
4x 2 2 2
fx 1
3x 2 2 3
3 4a 2
2, 3 ⇒ fx ax 2 2 3
Point: 1, 6 ⇒ 6 a1 2 2 3
6 9a 3
3 9a
1
3 a
(c) Area 100x x2 x 2 100x 2500 2500
x 50 2 2500
x 50 2 2500
The maximum area occurs at the vertex when x 50
and y 100 50 50. The dimensions with the
maximum area are x 50 meters and y 50 meters.
(b) The maximum revenue occurs at the vertex of the parabola.
b 800
$40
2a 210
R40 $16,000
The revenue is maximum when the price is $40 per unit.
The maximum revenue is $16,000.