a rectangular object 25 m wide is to pass under a parabolic arc that has width of 32m at the base and a height 24m at the center. If the vertex of the parabola is at the top ofbthe arch, what maximum height should the rectangular object have?

Answer 1

You know that the equation of the parabola is

y = 24-ax^2
Now plug in the point (16,0) to find a.
Now find y(12.5) to find the tallest object that will fit under the arch.

And of course, the vertex of the parabola will always be at the top of the arch!