Solved Applied Problems Parabola

Question

The cables of a suspension bridge are in the shape of a​ parabola, as shown in the figure. The towers supporting the cable are 500 feet apart and 100 feet high. If the cables touch the road surface midway between the​ towers, what is the height of the cable at a point 125 feet from the center of the​ bridge?

The cable is ______ feet from the road surface at a point 125 feet from the center of the bridge.

​(Simplify your​ answer.)

Answer 1

Set the parabola on the x-y axis with the vertex at (0,0). For standard form:

y = ax²

We know y is 100 when x is 250, so

a = 250²/100 = 1/625

y = x²/625

y(125) = 125²/625 = 25 feet