College Algebra 9th txtbk

SECTION 3–4 Quadratic Functions 215
Table 4
Length of Skid
Marks (in feet)
Speed Wet Dry
(mph) Asphalt Concrete
20 22 16
30 49 33
40 84 61
50 137 94
60 197 133
conditions at the time of the accident. Investigators conduct tests to determine skid mark
length for various vehicles under varying conditions. Some of the test results for a particular
vehicle are listed in Table 4.
Using the quadratic regression feature on a graphing calculator, (see the Technology
Connections following this example) we find a model for the skid mark length on wet
asphalt:
where x is speed in miles per hour.
L(x) 0.06x 2 0.42x 6.6
(A) Graph y L(x) and the data for skid mark length on wet asphalt on the same
axes.
(B) How fast (to the nearest mile) was the vehicle traveling if it left skid marks 100 feet
long?
SOLUTIONS
(A)
y L(x) 0.06x 2 0.42x 6.6
Skid mark length (feet)
300
50
(40, 84)
(30, 49)
(20, 22)
10 80
Speed (mph)
(60, 197)
(50, 137)
x
(B) To approximate the speed from the skid mark length, we solve
L(x) 100
0.06x 2 0.42x 6.6 100
0.06x 2 0.42x 93.4 0
Subtract 100 from both sides.
Use the quadratic formula.
x (0.42) 2(0.42)2 4(0.06)(93.4)
2(0.06)
0.42 122.5924
0.12
x 43 mph
The negative root was discarded.
MATCHED PROBLEM 10
A model for the skid mark length on dry concrete in Table 4 is
where x is speed in miles per hour.
M(x) 0.035x 2 0.15x 1.6
(A) Graph y L(x) and the data for skid mark length on dry concrete on the same
axes.
(B) How fast (to the nearest mile) was the vehicle traveling if it left skid marks 100 feet
long?