# What is the vertex form of y=x^2-12x+6?

Mar 9, 2016

$y = {\left(x - 6\right)}^{2} - 30$

#### Explanation:

The standard form of a quadratic function is $a {x}^{2} + b x + c$

the equation $y = {x}^{2} - 12 x + 6 \text{ is in this form }$

with a = 1 , b = -12 and c = 6

The vertex form is : $y = a {\left(x - h\right)}^{2} + k$

where (h,k) are the coords of vertex

the x-coord of vertex ( h ) = $\frac{- b}{2 a} = \frac{12}{2} = 6$

and y-coord( k) = ${6}^{2} - 12 \left(6\right) + 6 = - 30$

now (h , k ) = (6 , -30) and a = 1

$\Rightarrow y = {\left(x - 6\right)}^{2} - 30 \text{ is vertex form }$