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Math Help - Determining the equation of a parabola

  1. #1
    Junior Member
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    Determining the equation of a parabola

    I'm asked to give the equation of a parabola when both the top (maximum?*) and a point on the line are given. The general form of a parabola with top (x_{top}, y_{top}) is given: y = a(x - x_{top})^2 + y_{top}.

    Seems straightforward enough and when try to solve this, for example, for T =  (0, 0), P = (1, 2), I just fill in the blanks and solve for a: 2 = a(1 - 0)^2 + 0 \Leftrightarrow 2 = a * 1 \Leftrightarrow a = 2 \Leftrightarrow y = 2x^2 this sure enough works out as I would've expected.

    But then I'm asked to solve for the following: T = (3, 0), P = (-1, -2). Filling in tells me: -2 = a(-1 - 3)^2 + 0 \Leftrightarrow -2 = a * 16 \Leftrightarrow a = -\frac{1}{8} Leaving me to conclude that y= -\frac{1}{8}x^2, which according to my textbook is very wrong, it should be: y = -\frac{1}{8}x^2 + \frac{3}{4}x - \frac{9}{8}.

    Obviously I'm doing this wrong, so I'm looking for some pointers on how to approach a problem like this.


    *As English isn't my native language it's possible I confuse terms, in spite of trying to find a fitting translation. I apologise for that on beforehand and hope you would be able to correct me if I do so.
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  2. #2
    Senior Member Stroodle's Avatar
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    Re: Determining the equation of a parabola

    You disregarded the translation. You need to expand y=-\frac{1}{8}(x-3)^2
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  3. #3
    Junior Member
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    Re: Determining the equation of a parabola

    Ah, that makes sense

    y = -\frac{1}{8}(x - 3)^2 \Leftrightarrow y = -\frac{1}{8}(x^2 - 6x + 9) \Leftrightarrow y = -\frac{1}{8}x^2 + \frac{3}{4}x - \frac{9}{8}.

    Thanks
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