You live under a bridge that goes over a river. the underneath side of the bridge is an arc that can be modeled with the function y=-0.000407x^2+0.658x.Where x and y are in feet.

How high is the bridge?

How long is the section of bridge above the arc?

2 answers

y = x (.658 - .000407 x)
where is y = 0 ?
at x = 0 and at x = .658/.000407 = 1617 ft long (that is part B)
this is a parabola that crosses the x axis at 0 and 1617
so the vertex, max height, is halfway between
at x = 808 what is the height?
y = -.000407 (808^2) + .658(808)
= 266 feet high (Part A)
correct answer is "The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,791.58 ft."