# How do you write this equation into the vertex form f(x) = x^2+4x+6?

Jun 12, 2018

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

#### Explanation:

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

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

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

$\text{to obtain this form "color(blue)"complete the square}$

$f \left(x\right) = {x}^{2} + 4 x \textcolor{red}{+ 4} \textcolor{red}{- 4} + 6$

$\textcolor{w h i t e}{f \left(x\right)} = {\left(x + 2\right)}^{2} + 2 \leftarrow \textcolor{b l u e}{\text{in vertex form}}$