Question: A tunnel with a parabolic arch is 12 m wide. If the height of the arch 4 m from the left edge is 6 m, can a truck that is 5 m tall and 3.5 m wide pass through the tunnel? Justify your decision.

Question

I drew the graph of the arch with x-intercepts (0,0) and (12,0) , and with the point (4,6) on it.I know that a truck can go through the tunnel because there is a known point that is taller than 5 m, but how do I show my work?

Thanks in advance!

Answer 1

Assume that the axis of symmetry is
x = 6. There are 6 points of interest:

Top: P1(4 , 6) , P2(6, 6) , P3(8 , 6).

Bottom:P4(4 , 0) , P5(6 , 0) P6(8 ,0).
These two lines represent the hor.
lines of a rectangle. Add these points
to your sketch.

Width = X3 - X1 = X6 - X4 = 8 - 4 = 4m
Height = Y1 - Y4 = Y2 - Y5 = Y3-Y6 =
6 - 0 = 6m.

Yes, he or she can drive atruck through; but there is no room for
error!