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Math Help - Parabolic Arch

  1. #1
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    Parabolic Arch

    Parabolic Arch-0329131618.jpg
    f 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
    MHF Contributor

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    Re: Parabolic Arch

    You can answer your question yourself with a little thought: Yes, setting up a coordinate system so that the center of the bridge is at the origin, the parabola is of the form y= ax^2. When x= 10, at the shore, y= -10 so you must have -10= a(10^2)= -100a. Dividing both sides by -100, a= -1/10 so the equation is y= -x^2/10. Now, in that coordinate system, "2 feet from the shore" is x= 8 or x= -8.
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