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Math Help - Parabolic Arch

  1. #1
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    Parabolic Arch

    Parabolic Arch-0329131618.jpg
    If you can't read it, "A horizontal brige is in the shape of a parabolic arch. Given the information in the picture below, what is the height of the arch 2 feet from the shore?

    Please help!!
    Thank you
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Parabolic Arch

    Quote Originally Posted by BrendaB View Post
    Click image for larger version. 

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    If you can't read it, "A horizontal brige is in the shape of a parabolic arch. Given the information in the picture below, what is the height of the arch 2 feet from the shore?

    Please help!!
    Thank you
    Hi BrendaB!

    You would use x-h=8, which is the distance from the origin labeled as B.
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  3. #3
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    Re: Parabolic Arch

    If you put the left hand corner at the origin, then you have three points, namely the two x intercepts (0, 0) and (20, 0), and the turning point (10, 10).

    The turning point form of the equation will be the easiest to use, \displaystyle y = a\left( x - h \right)^2 + k. You have (h, k) = (10, 10) and after substituting these and another point as (x, y) you can get the value of a.

    Once you have the equation of your curve, set y = 2 and solve for x.
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