a) Find a quadratic function that fits the data on the right. 60 25 Travel Speed
ID: 2894705 • Letter: A
Question
a) Find a quadratic function that fits the data on the right.
60
25
Travel Speed
(mph)
Braking Distance
(ft)
30
20
50
100
70
295
a)
y(x)=
(Use integers or decimals for any numbers in the expression. Do not round until the final answer. Then round to three decimal places as needed.)
b) _____ft
(Round to one decimal place as needed.)
c) Choose the correct answer below.
A.
No, because the model shows decreasing stopping distances for speeds from 0 to
2525
mph.
B.
Yes, because the quadratic reqression equation closely predicts stopping distance for any given speed.
C.
Yes, because
2525
is a member of the function's domain.
D.
No, because the function is only good for the given speeds of
3030
mph,
5050
mph, and
7070
mph.
a) Find a quadratic function that fits the data on the right.
b) Use the function to estimate the braking distance of a car that travels at60
mph. c) Does it make sense to use this function when speeds are less than25
mph? Why or why not?Travel Speed
(mph)
Braking Distance
(ft)
30
20
50
100
70
295
Explanation / Answer
1)
let travel speed be x ,braking distance be y
general quadratic function is y =ax2+bx +c
a302+b30 +c=20 => 900a+30b +c=20
a502+b50 +c=100 => 2500a+50b +c=100
a702+b70 +c=295 => 4900a+70b +c=295
2500a+50b +c-900a-30b -c=100-20
=>1600a +20b=80
=>80a+b =4
=>b=4-80a
4900a+70b +c-2500a-50b -c=295-100
=>2400a+20b=195
2400a+20b=195 ,b=4-80a
=>2400a+20(4-80a)=195
=>2400a+80-1600a=195
=>800a=115
=>a=115/800
=>a=0.14375
b=4-80a ,a=0.14375
=>b=4-(80*0.14375)
=>b=-7.5
900a+30b +c=20 , a=0.14375 , b =-7.5
=>(900*0.14375)+(30*(-7.5)) +c=20
=>c=115.625
so quadratic equation is y=0.14375x2-7.5x+115.625
so quadratic equation is y=0.144x2-7.500x+115.625
2)
braking distance of a car that travels at 60 mph =y(60)
braking distance of a car that travels at 60 mph =(0.14375*602)-(7.5*60)+115.625
braking distance of a car that travels at 60 mph =183.1 ft
3)
when speed is 25mph
x=25
y=(0.14375*252)-(7.5*25)+115.625
y=17.96875
y(0)=115.625
y(0) >y(25)
A.
No, because the model shows decreasing stopping distances for speeds from 0 to 25 mph.
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