Question

The arch that supports a highway bridge that passes over a street forms a parabola whose height above the street in feet can be determined using the function h(x)= -2x2+12.
a) How wide is the street?
b) Could a truck that is 10 feet tall be able to pass under the bridge?
I am abosolutely stumped on this question. Would anyone be willing to guide me?

Answer 1

(a) the width of the street is the distance between the roots (where h=0)
(b) assuming a zero-width truck, check the vertex of the parabola, which is, of course, midway between the roots, at x=0

Did you at least draw the graph?

Answer 2

Oh! Yes, I did. I just couldn't wrap my head around the question, I guess.
How would I find the distance between the roots? Would I need to find then first?