Math

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.

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!

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  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!

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