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.
:
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 = {{{(-.8)/512}}}
a = -.0015625
:
Difference of squares, so don't worry about b, the equation is
y = -.0015625x^2 + .4
:
Looks like this:
{{{ graph( 300, 200, -20, 20, -1, 1, -.0015625x^2+.4) }}}