SOLUTION: Roads are designed with parabolic surfaces to allow rain to drain off. A particular road that is 32" feet wide is 0.4 foot higher in the center that it is on the sides. Find the eq
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Question 215273: Roads are designed with parabolic surfaces to allow rain to drain off. A particular road that is 32" feet wide is 0.4 foot higher in the center that it is on the sides. Find the equation of the parabola that models the the road surface by assuming that the center of the parabola is at the origin.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Roads are designed with parabolic surfaces to allow rain to drain off.
A particular road that is 32" feet wide is 0.4 foot higher in the center that it is on the sides.
Find the equation of the parabola that models the the road surface by assuming
that the center of the parabola is at the origin.
:
Find the equation using the form: ax^2 + bx + c = y
We know this will be the difference of squares; c = +.4
x = -16; y = 0
(-16^2)a - 16b + .4 = 0
256a - 16b + .4 = 0
and
x = +16; y = 0
(16^2)a + 16b + .4 = 0
256a + 16b + .4 = 0
:
Add the two equations, eliminate b, find a
256a + 16b + .4 = 0
256a - 16b + .4 = 0
--------------------
512a + .8 = 0
512a = -.8
a =
a = -.0015625
:
Difference of squares, so don't worry about b, the equation is
y = -.0015625x^2 + .4
:
Looks like this:
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