# How do you find the axis of symmetry and vertex point of the function: y=x^2+12x-9?

Oct 8, 2015

Axis of Symmetry: $x = - 6$
Vertex: $\left(- 6 , - 45\right)$

#### Explanation:

The first thing you must do, is convert this equation to vertex form $y = a {\left(x - h\right)}^{2} + k$. Finding the axis of symmetry and the vertex will become easy after that.

Converting to Vertex Form ($y = a {\left(x - h\right)}^{2} + k$)
$y = {x}^{2} + 12 x - 9$
$y + 9 = {x}^{2} + 12 x$
$y + 9 + 36 = {x}^{2} + 12 x + 36$
$y + 45 = {\left(x + 6\right)}^{2}$
$\textcolor{red}{y = {\left(x + 6\right)}^{2} - 45}$

Axis of Symmetry
The axis of symmetry is $x = h$. Just by looking at the equation in vertex form, you will see that $h = - 6$.

Therefore, the axis of symmetry is:

$x = h$
$\textcolor{b l u e}{x = - 6}$

Vertex
The vertex is $\left(h , k\right)$. Again, just look at the equation and you will see that $h = - 6$ and $k = - 45$.

Therefore, the vertex is:

$\left(h , k\right)$
color(magenta)((-6,-45)