A simply supported beam is 64 feet long and has a load at the center (see figure). The deflection (bending) of the beam at its center is 1 inch. The shape of the deflected beam is parabolic. https://www.webassign.net/larprecalcaga5/10-1-090.gif
(a) Find an equation of the parabola. (Assume that the origin is at the center of the beam. Express x and y in feet.)
(b) How far from the center of the beam is the deflection equal to 1/3 inch? (Round your answer to one decimal place.)
I know that the answer to a is y=(1/12288)x^2, but I have absolutely no idea why.
I have no idea how to go about solving b.
Any information is much appreciated, thanks :)