# What is the vertex form of y=x^2-4x-12 ?

Feb 14, 2016

$y = {\left(x - 2\right)}^{2} - 16$

#### Explanation:

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

the equation here $y = {x}^{2} - 4 x - 12 \textcolor{b l a c k}{\text{ is of this form }}$

by comparison : a = 1 , b = -4 and c = -12

The vertex form of the quadratic function is

$y = a {\left(x - h\right)}^{2} + k$
where (h , k ) are the coords of the vertex.

the x-coord of the vertex = $- \frac{b}{2 a} = - \frac{- 4}{2} = 2$
substitute x = 2 into original function for y-coord.

y = ${\left(2\right)}^{2} - 4 \left(2\right) - 12 = 4 - 8 - 12 = - 16$
hence (h , k )= (2 , -16 ) and a = 1

$\Rightarrow y = {\left(x - 2\right)}^{2} - 16$
graph{x^2-4x-12 [-40, 40, -20, 20]}