Question

A parabolic lattice arch is 8 feet high at the vertex. At a height of 4 feet, the width of the lattice is 4 ft. How wide is the lattice arch at ground level?

Answer 1

The arch is in the shape of an inverted parabola. The equation of the arch is found as follows:
$y=-ax^{2}+8$
Substituting the values at a height of 4 ft, we get:
4 = -4a + 8
a = 1
At ground level y = 0:
$0=-x^{2}+8$
$x=+- \sqrt{8}$
therefore the width of the arch at ground level is:
$2 \sqrt{8} \ feet$