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

An example would be:

$\displaystyle -x^2 + 5x - 1$

A step-by-step view would really help :]

Thank you (:

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- Dec 9th 2008, 10:49 PMmeiyukichanVertex Form
I know that the vertex form is $\displaystyle y = a(x - h)^2 + k$, but I don't understand how to get an expression into vertex form.

An example would be:

$\displaystyle -x^2 + 5x - 1$

A step-by-step view would really help :]

Thank you (: - Dec 9th 2008, 11:08 PMmr fantastic
Complete the square:

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

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

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