# What is the the vertex of y=(x -4)^2 + 12x -36?

Mar 21, 2017

$y = {\left(x - 2\right)}^{2} - 24$ is the equation in vertex form.

#### Explanation:

Vertex form of equation is of the type $y = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is the vertex and axis of symmetry is $x - h = 0$
Here we have

$y = {\left(x - 4\right)}^{2} + 12 x - 36$

$= {x}^{2} - 8 x + 16 + 12 x - 36$

$= {x}^{2} + 4 x - 20$

$= {x}^{2} + 2 \times 2 x + {2}^{2} - 4 - 20$

$= {\left(x - 2\right)}^{2} - 24$

Hence, $y = {\left(x - 2\right)}^{2} - 24$ is the equation in vertex form. Vertex is $\left(2 , - 24\right)$ and axis of symmetry is $x - 2 = 0$
graph{(x-2)^2-24-y=0 [-10, 10, -30, 10]}