A simply supported beam is a = 80 feet long and has a load at the center (see figure). The deflection of the beam at its center is 1 inch. The shape of the deflected beam is parabolic.

A person is standing on a support beam on top of a scaffold. The person is standing at the center of the support beam that is labeled a. The support beam goes down a distance of 1 inch in the center with the person standing on it.

(a)Write an equation of the parabola with its vertex at the origin that models the shape of the beam. (Let x represent horizontal distance in feet and let y represent vertical distance in feet.)
_____

(b)How far from the center of the beam (in feet) is the deflection 1/2 inch? (Round your answer to one decimal place.)
_____ ft