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Math Help - Trying to find equation for parabola

  1. #1
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    Trying to find equation for parabola

    Vertex of 0,3
    Focus of 0,0
    Formula for parabola:
    y = a(x - h)^2 + k

    I assume that h = 0, k = 3 (the vertex)
    how does the focus factor into this equation? thanks.
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  2. #2
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    Re: Trying to find equation for parabola

    Quote Originally Posted by togo View Post
    Vertex of 0,3
    Focus of 0,0
    Formula for parabola:
    y = a(x - h)^2 + k

    I assume that h = 0, k = 3 (the vertex)
    how does the focus factor into this equation? thanks.
    If you write the eqation of a parabola as y= a(x- x_0)^2+ y_0^2, the same as your formula with [itex]h= x_0[/itex], [itex]k= y_0[/tex], where [itex](x_0, y_0)[/itex] is the vertex, then the focal length is f= 1/4a.Parabola - Wikipedia, the free encyclopedia

    Saying that the vertex is at (0, 3) and the focus is at (0, 0) means that the focal length is f=1/4a= 3 so that 4a= 1/3, a= 1/12. Of course, because the focus is below the vertex, the parabola opens downward, so a is negative.
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