Question 191817: (a) Find a quadratic function that fits the following data. (b) Use the function to estimate the number of daytime accidents that occur at 50km/h
Travel Speed #of daytime accidents
(in km/hr) (for every 200 million km driven)
60 100
80 130
100 200
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! form is y=Ax^2 +Bx +C
subst in data
1) 100=A60^2 +B60 +C
2) 130 = A80^2+B80 +C
3) 200=A100^2 +B100+C
subt (1) - (2) results in 30=A(80^2-60^2) +B(80-60)=2800A+20B
subt (3)-(2) results in 70 = A(100^2-80^2) +B(100-80) = 3600A+20B
subt the two above results in
40 = 800A, or A=.05
Subst into (1)-(2) above , 30=.05(2800)+20B
30-140=20B
B=(-5.5)
Subst these into (1) 100=(.05)(60^2) - (5.5)(60)+C
100=180-330+C
C=(250)
combining y+.05x^2 -5.5x+250
checking input data 60/100, 80/130,100/200,
using x=50 results in y=100 (yes same as for 60)
checking at x=55, y=98.75 so yes there is a vertex between x=50 and x=60
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