# What is the vertex form of y=x^2 + 12x + 36?

Nov 24, 2017

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

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

$\text{to obtain this form use the method of}$
$\textcolor{b l u e}{\text{completing the square}}$

• " ensure the coefficient of the "x^2" term is 1 which it is"

• " add/subtract "(1/2"coefficient of x-term")^2
$\text{to } {x}^{2} + 12 x$

${x}^{2} + 2 \left(6\right) x \textcolor{red}{+ 36} \textcolor{red}{- 36} + 36$

$= {\left(x + 6\right)}^{2} + 0 \leftarrow \textcolor{red}{\text{in vertex form}}$

Nov 24, 2017

$y = {\left(x - 0\right)}^{2} - 6$

#### Explanation:

YOUR EQUATION: $f \left(x\right) = a {x}^{2} + b x + c$
VERTEX FORM: $f \left(x\right) = a {\left(x - h\right)}^{2} + k$

1. Find the vertex $\left(h , k\right)$
Number 2-3 tells you how to find the vertex
Remember $a = 1$

2. Find -b/2a (this is how to find $h$)
In this equation -b/2a would be -12/2(1)
The answer to -12/2(1) would be -6.

3. Find $k$ by plugging in the answer for $h$ into the equation.
$y = {x}^{2} + 12 x + 36$
$y = {\left(- 6\right)}^{2} + 12 \left(- 6\right) + 36$
$y = - 36 + 36$
$y = 0$
$h$ would be $0$

4. Plug the answers into vertex form
$y = 1 {\left(x - 0\right)}^{2} - 6$
$y = {\left(x - 0\right)}^{2} - 6$