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 (:
Complete the square:
$\displaystyle y = - (x^2 - 5x + 1) = - \left(\left[x - \frac{5}{2}\right]^2 - \left(\frac{5}{2}\right)^2 + 1\right)$
$\displaystyle = - \left(\left[x - \frac{5}{2}\right]^2 - \frac{25}{4} + 1\right) = - \left(\left[x - \frac{5}{2}\right]^2 - \frac{21}{4}\right)$
$\displaystyle = - \left(x - \frac{5}{2}\right)^2 + \frac{21}{4}$.