Calculus

A parabolic arch bridge has a 60ft base and a height of 24ft. Find the height of the arch at a distance of 5, 10, and 20 ft from the center

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  1. let the vertex of the parabola be (0,60)
    its equation would be
    y = ax^2 + 60 , but (30,0) and (-30,0) would also lie on it

    0 = a(900) + 60
    a = -60/900 = -1/15

    equation of bridge is
    y = (-1/15)x^2 + 60

    so when x = 5
    y = (-1/15)(25) + 60 = 175/3 ft
    or 58 1/3 ft
    or appr 58.33 ft

    repeat for x = 10 and x = 20

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