Quadratic Function Application Question

Question

A bridge forms a parabolic arch. The span of the arch is 60m and it’s center is 10m above either end. a) Write a quadratic function for this bridge. b) What is the height of the arch 15m from either end of the bridge?

Answer 1

Place the origin aligned with the peak of the bridge. x varies between -30 and 30 m and the y intercept is (0,10). The quadratic is in the form y = y₀ - cx² (positive c and x is centered on 0)

From y₀ = 10 and y(30) = 0: 0 = 10 - c(900) and c =1/90

y = 10 -(1/90) x²

Plug in to find y(15). I actually found the equation this way y = 10 - 10 (x/30)^{2 (}knowing that I had to cancel the 10 at x=30)

Hope that helped.