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Math Help - I need and explaination

  1. #1
    niniu_blue
    Guest

    I need and explaination

    I have not taken a math class for two years and need a little refreshing.

    Find the standar equation of a parabola that has a vertical axis and satisfies the given conditions.

    Vertex (3,5) x-intercept 0

    I need help solving this and an explaination on how to solve equations like this in general. Thanks!!
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by niniu_blue View Post
    I have not taken a math class for two years and need a little refreshing.

    Find the standar equation of a parabola that has a vertical axis and satisfies the given conditions.

    Vertex (3,5) x-intercept 0

    I need help solving this and an explaination on how to solve equations like this in general. Thanks!!
    Something wrong with the Question. x-intercept is what? It is 0 only? That is incomplete.

    However, if that is all that is given, and the Question is complete or is posted correctly, then "x-intercept 0" may mean the origin (0,0) is an x-intercept.

    The standard form of the squation of a "vertical" parabola--or a parabola whose axis of symmetry is vertical--is
    (y-k) = a(x-h)^2 ------------(i)
    where
    (h,k) is the vertex.
    "a" is any real number.

    So if the vertex is at point (3,5), the Eq.(i) becomes
    (y -5) = a(x -3)^2 ---------(ii)

    What is "a"?
    At the x-intercept (0,0), Eq.(ii) becomes
    (0 -5) = a(0 -3)^2
    -5 = 9a
    a = -5/9 --------------***

    Therefore, the parabola is
    y -5 = (-5/9)(x -3)^2 ---------------answer.
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