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Math Help - Vertex Form

  1. #1
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    Vertex Form

    I know that the vertex form is y = a(x - h)^2 + k, but I don't understand how to get an expression into vertex form.

    An example would be:
    -x^2 + 5x - 1


    A step-by-step view would really help :]
    Thank you (:
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  2. #2
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    Quote Originally Posted by meiyukichan View Post
    I know that the vertex form is y = a(x - h)^2 + k, but I don't understand how to get an expression into vertex form.

    An example would be:
    -x^2 + 5x - 1


    A step-by-step view would really help :]
    Thank you (:
    Complete the square:

    y = - (x^2 - 5x + 1) = - \left(\left[x - \frac{5}{2}\right]^2 - \left(\frac{5}{2}\right)^2 + 1\right)

     = - \left(\left[x - \frac{5}{2}\right]^2 - \frac{25}{4} + 1\right) = - \left(\left[x - \frac{5}{2}\right]^2 - \frac{21}{4}\right)

     = - \left(x - \frac{5}{2}\right)^2 + \frac{21}{4}.
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