Question

Help application of parabolas

Answer 1

A support cable for a bridge is parabolic in shape. The cable is supported by two 25 meter tall towers that are 80 meters apart. The lowest point on the cable is 5 meters above the bridge surface (the x-axis). Several vertical supports connect the cable to the base of the bridge. Determine the length of a vertical support located 25 meters from the left tower. Consider that the bridge is symmetric about the y-axis.

Answer 2

the bridge is symmetrical about the y- axis, then consider using the quadratic eqn in standard form to solve it.
the vertex (p,q) is at (0,5) so the eqn is:
y = a(x - 0) + 5, since a is unknown, the find it by substituting a point in:

25 = a(40)^2 + 5
20 = 1600a
0.0125 or 1/80 = a

now substitute in the unknown point value at 25 m away from the left tower P(-15,y) so:
y = 1/80(-15 - 0)^2 + 5
y = 7.8125 I hope this might help

Answer 3

sorry if this is not what you whant

Answer 4

I was trying to plot it out in my head aha. Thank you for the explanation