# How do you find the vertex of a parabola f(x)=x^2+7x+6?

Jul 8, 2015

The vertex is located at $\left(- \frac{7}{2} , - \frac{25}{4}\right)$

#### Explanation:

Given $f \left(x\right) = {x}^{2} + 7 x + 6$

Complete the square
$\textcolor{w h i t e}{\text{XXXX}}$$= {x}^{2} + 7 x + {\left(\frac{7}{2}\right)}^{2} - {\left(\frac{7}{2}\right)}^{2} + 6$
Simplify into vertex form
$\textcolor{w h i t e}{\text{XXXX}}$$= {\left(x + \frac{7}{2}\right)}^{2} - \frac{25}{4}$
or
$\textcolor{w h i t e}{\text{XXXX}}$$= {\left(x - \left(- \frac{7}{2}\right)\right)}^{2} + \left(- \frac{25}{4}\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$which is the vertex form with vertex at $\left(- \frac{7}{2} , - \frac{25}{4}\right)$