# How do you write g(x)=2x^2+8x+13 in vertex form?

Aug 25, 2017

$g \left(x\right) = 2 {\left(x + 2\right)}^{2} + 5$

#### Explanation:

$\text{given the parabola in standard form } a {x}^{2} + b x + c$

$\text{the x-coordinate of the vertex is}$

${x}_{\textcolor{red}{\text{vertex}}} = - \frac{b}{2 a}$

$2 {x}^{2} + 8 x + 13 \text{ is in standard form}$

$\text{with } a = 2 , b = 8 , c = 13$

$\Rightarrow {x}_{\textcolor{red}{\text{vertex}}} = - \frac{8}{4} = - 2$

$\text{substitute this value into the equation for y-coordinate}$

$\Rightarrow {y}_{\textcolor{red}{\text{vertex}}} = 2 {\left(- 2\right)}^{2} + 8 \left(- 2\right) + 13 = 5$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 2 , 5\right)$

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

•color(white)(x)y=a(x-h)^2+k

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

$\text{here "a=2" and } \left(h , k\right) = \left(- 2 , 5\right)$

$\Rightarrow g \left(x\right) = 2 {\left(x + 2\right)}^{2} + 5 \leftarrow \textcolor{red}{\text{ in vertex form}}$