Parabola Problem 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.

Parabola Problem 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. < image description here]( (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 :)

Since the parabola's vertex is the origin and we're talking of an upwards parabola, it looks like $\;y=ax^2\;,\;\;a>0\;$ . Now observe the parabola passes through the point $\;(32\cdot12,1)\;$ (in inches and assuming we indeed have $\;12\;$ inches in one feet)..

Find now $\;a\;$ and yoour parabola's formula.