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

1. A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 inches deep, where will the collected light be concentrated?

2. 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 630 feet high and 630 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 arch.
(b)The table below gives the height of the Arch at various widths; find the corresponding heights for the parabola found in (a).

 

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

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