Question

An arch shaped monument 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 475 feet high and 456 feet wide at its base. Complete parts​ (a), (b), and​ (c).

​(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 gives the height of the arch at various​ widths; find the corresponding heights for the parabola found in​ (a).

width (ft)	height (ft)
367	100
318	212.5
228	325

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

Answer 1