The Gateway Arch in St. Louis is often mistaken to be parabolic in shape. In fact, it is a catenary, which has a more complicated formula than a parabola. The Arch is 625 feet high and 598 feet wide at its base. 

(a) Find the equation of a parabola with the same dimensions. Let x equal the horizontal distance from the center of the arc. 

(b) The table below gives the height of the Arch at various widths; find the corresponding heights for the parabola found in (a). 

Width (ft)...................Height(ft)

568.............................100

478.............................312.5

308.............................525

(c) Do the data support the notion that the Arch is in the shape of a parabola?