STATEMENT OF PROBLEM

The Gateway Arch in St. Louis is in the shape of a catenary -- a function of the form f(x) = fc - A(cosh[c x/L] - 1)

where A = fc/[(Qb/Qt) - 1] = 68.7672,
c = arccosh(Qb/Qt) = 3.0022,
fc = Max. Height of Centroid = 625.0925,
Qb = Max cross-section at arch base = 1262.6651,
Qt = Min cross-section at arch top = 125.1406,
L = half of centroid at arch base = 299.2239.

All measurements are given in feet. This is actually the shape of the centroid of the arch -- the set of points going through the center of the arch. The data was provided by the National Park Service.

At first glance, the casual observer might mistake the shape of the St. Louis Arch for a parabola. Test the observation by seeing how closely you can fit a parabola to the arch. Defend your notion of close.