Math

An engineer is designing a parabolic arch. The arch must be 15 m high, and 6 m wide at a height of 8 m. a) Determine a quadratic function that satisfies these conditions.

I've got : 8=a(6-h)^2+15, but i don't know what to do next.

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asked by Emily
  1. I will assume that your equation is such that the vertex is on the y-axis

    Then your equation will be

    y = ax^2 + 15 , (the h of your equation will be zero)
    then (6,8) must lie on the equation

    8 = a(6)^2 + 15
    a = -7/36

    equation: y = (-7/36)x^2 + 15

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  2. the peak is at 3,15, it turns downward so that at h=8 me the difference in x is 6.

    h=-a(x-3)^+15
    then
    8=-a(6-3)^2+15
    8=-9a+15
    a=7/9

    so, here is one that satisfies the statement
    h=-7/9 (x-3)^2+15

  3. Bobpursley, how do you know that the peak is at (3,15)?

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    posted by Emily
  4. i don't know howto solve this either someone HELP

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