I am studying a practice exam and this is one of the problems:

To get to the castle they had to go through a bridge shaped like a parabolic arch. The arch measured 30 ft at its highest point. Now a road goes through the arc 40 ft wide and must have a clearance of 10 ft or their truck would hit the arch as it was going through. Determine the distance across the base of the arch. Sketch the bridge for me.

I understand the center is at 0,0. I know I need to put this into x^2=4P(y)

What I am having trouble with is finding the X or Y I need to put into the equation. I keep finding more points each time I read this equation and now I am just confused. My book gives ONE example of an equation like this but it is set up differently.

I think (20, -20) lies on the curve but when I put this into the equation I get lost on how to do it.

20^2= 4P (20) ?

If I do this I end up with the road width but I need the base distance. I know for that I would need to double the equation but I cannot figure it out.

thanks so much for any help! Quiz is tomorrow and explanation would be greatly appreciated.

Two things:

1. If the road extends from -20<=x<=+20, and a 10-foot high truck must clear, then the points (-20,10) and (20,10) both lie on the curve.
2. The equation is of the form (y-Y_0) = P(x-X_0)^2, where (X_0,Y_0) is the apex, which in this case is (0,30). So you need to find the value of P that satisfies:

y-30 = Px^2