# What is the vertex form of y=x^2-6x+6?

Mar 12, 2015

The vertex form of an equation is in the form:
$y = {\left(x + a\right)}^{2} + b$

${\left(x - a\right)}^{2}$ when expanded is ${x}^{2} - 2 a x + {a}^{2}$

for the given equation, it follows that
$2 a x = - 6 x$
$\rightarrow a = - 3$

${\left(x - 3\right)}^{2} = {x}^{2} - 6 x + 9$

comparing this to the given equation, we see that
$b = - 3$

So the vertex form of the given equation is
$y = {\left(x - 3\right)}^{2} - 3$