Question

A man wants to create a Japanese garden with a parabolic footbridge to cross the creek in front of his garden. The bridge needs to span 5 meters and - according to the design he has selected - is 2 meters tall at the apex. Find a quadratic model that describes the shape of the bridge.

Answer 1

If we place the vertex at (0,2), then

y = 2-ax^2
Since the span is 5 meters, the roots are at x = ±5/2

So, 2 - 25/4 a = 0
a = 8/25

y = 2 - 0.32x^2