# How do you write the vertex form equation of the parabola y = x^2 + 8x - 1?

##### 1 Answer
Jun 1, 2017

$y = {\left(x + 4\right)}^{2} - 17$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ( h , k ) are the coordinates of the vertex and a is a constant.

$\text{for the standard form of a parabola } y = a {x}^{2} + b x + c$

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

$\text{here } a = 1 , b = 8 , c = - 1$

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

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

$\Rightarrow {y}_{\textcolor{red}{\text{vertex}}} = {\left(- 4\right)}^{2} + 8 \left(- 4\right) - 1 = - 17$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 4 , - 17\right)$

$\Rightarrow y = {\left(x + 4\right)}^{2} - 17 \leftarrow \textcolor{red}{\text{ in vertex form}}$