You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y=-0.000475x^2+0.851x, where x and y are in feet. How high above the river is the bridge(the top of the arch)? How long is the section of bridge above the arch? How long is the section of bridge above the arch?

Question

You live near a bridge that goes over a river. The underside of the bridge is an arch that can be modeled with the function y=-0.000475x^2+0.851x, where x and y are in feet. How high above the river is the bridge(the top of the arch)? How long is the section of bridge above the arch?   How long is the section of bridge above the arch?

Steve · Answer

y = x(-.000475x+.851)
y=0 at x=0,1791
The vertex is midway between the roots
So, at x=896, y=381

The length of the bridge is the distance between the roots. (assuming the bridge just touches the river banks at the water's edge -- not too likely in the real world)