a question on my college math homework

Question

A suspension bridge with weight uniformly distributed along its length has twin towers that extend

85

meters above the road surface and are

1600

meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point

400

meters from the center. ​ (Assume that the road is​ level.)

Answer 1

If the suspension cables touch the roadway at exactly halfway, we can treat the roadway like the x-axis.

Which makes that point (800, 0)

And makes the connections at the towers (0, 85) and (1600, 85)

If we use y = a (X - h)² + k to model this bridge,

h = 800, k = 0 but we don't know a yet

If we use y = aX² + bX + c,

then c = 85, but we don't know a or b

You can plug in (0,85) into the vertex form and solve to find the value of a.

85 = a (0 - 800)²

Solve for a

Write out your full y = equation

then plug in X = 400 to find the height, y.

(This height should match the height at X = 1200.)

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