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Math Help - Finding the correct equation for a parobola

  1. #1
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    Finding the correct equation for a parobola

    The Problem: Write an equation for a parabola with vertex (3, -6) crossing the x-axis at -1 and 7.

    Attempted Solution:

    The equation for a parobola is y = a(x- h)^2 + k.

    I plugged in the vertex.

    y=a(x-3)^2 - 6

    I do not know how I would find what value would equal both -1 and 7, thought. There doesn't appear to be any algebric method which would work, at least to my intuitions.

    Could someone please help?

    Thank you
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  2. #2
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    y = a(x - 3)^2 - 6

    (-1,0) is on the parabola ...

    0 = a(-1 - 3)^2 - 6

    0 = 16a - 6

    a = \frac{3}{8}

    (7,0) is on the parabola ...

    0 = a(7 - 3)^2 - 6

    0 = 16a - 6

    wow ... same value for "a".
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