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

86. (a) and (c)
(b)
(d) 1996
(e) Vertex occurs at
(f)
950
4
650
88. (a) and (c)
y 4.303x 2 49.948x 886.28
Minimum occurs at year 1996.
x 18
31
12
x b 49.948
5.8
2a 24.303
y 4.30318 2 49.94818 886.28 1381.388
There will be approximately 1,381,000 hairdressers
and cosmetologists in 2008.
10 80
20
(b)
Section 2.1 Quadratic Functions and Models 149
87. (a)
(b)
0
25
−5
0.002s 2 0.005s 0.029 10
a 2, b 5, c 10,029
s 5 ± 52 4210,029
22
s
y 0.0082x 2 0.746x 13.47
2s 2 5s 10,029 0
5 ± 80,257
4
s 72.1, 69.6
100
2s 2 5s 29 10,000
The maximum speed if power is not to exceed
10 horsepower is 69.6 miles per hour.
(d) The maximum of the graph is at x 45.5, or about 45.5 mi/h.
Algebraically, the maximum occurs at
x mi/h.
b 0.746
45.5
2a 20.0082
89. True. The equation 12x has no real solution,
so the graph has no x-intercepts.
2 1 0 90. True. The vertex of is and the vertex of
is 5
f x 4 gx
4 , 71 4 .
91.
ax2 b
f x ax
x c
a 2 bx c
ax2 b b2
x
a 4a
b f 2a
b2 b2
c
4a 2a
2 b2
b
ax
2a 2
b2
c
4a
ax b
2a 2 4ac b2
4a
b2 b
a4a2 b c
2a
b2 2b 2 4ac
4a
4a2 c
b 4ac b2
So, the vertex occurs at ,
2a
4ac b2
4a
4a
b b
, f 2a 2a .
5 53
, 4