Grade 11 Precalculus

Question

The towers supporting the cable of a suspension bridge are 100 m apart and 30 m above the bridge it supports. Supposedly, the cable hangs, following the shape of a parabola, with its low est point 5 m above the bridge. How high is the cable 40 m away from the center? Show your solutions and illustrations.

Answer 1

As Mark M stated in the comments, if yu just draw a diagram you should be able to figure it out. Here is a diagram. Can you see the parabola and the coordinate plane?

You can use the vertex form, y = a(x - h)² + k, using (h, k) as (0, 5) and then plug in either (-50, 30) or (50, 30) to determine what "a" is. Once you have the equation, you can plug in x = -40 to determine what "h" is.