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Math Help - Need help with writing a quadratic equation

  1. #1
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    Need help with writing a quadratic equation

    I am given the following info:

    2 x-intercepts: (3,0) (9,0)
    there is a maximum occurring at 2

    I figured I would use the equation y=a(x-p)(x-q)

    so I plugged in the two x-ints

    y=a(x-3)(x-9)

    Now my question is that if I know that the maximum is 2, where exactly would that go in the equation?
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  2. #2
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    Quote Originally Posted by coolieman View Post
    I am given the following info:

    2 x-intercepts: (3,0) (9,0)
    there is a maximum occurring at 2

    I figured I would use the equation y=a(x-p)(x-q)

    so I plugged in the two x-ints

    y=a(x-3)(x-9)

    Now my question is that if I know that the maximum is 2, where exactly would that go in the equation?
    Hello,

    you've got the 2 zeros of the quadratic function. That means the vertex of the corresponding parabola is at x_V\left(\frac{3+9}{2}, a(6-3)(6-9)  \right).

    If I understand your problem correctly the maximum is 2 and that is only possible if this is the y-value of the vertex. Thus:

    a(6-3)(6-9) = 2~\Longrightarrow~-9a = 2~\Longrightarrow~a = -\frac{2}{9}

    The complete equation of the quadratic function is now:

    p(x)=-\frac{2}{9}(x-3)(x-9) =\boxed{ -\frac{2}{9}x^2+\frac{8}{3}x - 6}
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