Vertex Form

Quote:

Originally Posted by meiyukichan

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:

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

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

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