# How do you find the VERTEX of a parabola y=x^2+7x+12?

Sep 8, 2015

Use the method of completing the square to convert to vertex form and get the vertex at $\left(- \frac{7}{2} , - \frac{1}{4}\right)$

#### Explanation:

Vertex form: $y = m {\left(x - a\right)}^{2} + b$ with vertex at $\left(a , b\right)$

$y = {x}^{2} + 7 x + 12$

$\rightarrow y = {x}^{2} + 7 x + {\left(\frac{7}{2}\right)}^{2} + 12 - {\left(\frac{7}{2}\right)}^{2}$

$\rightarrow y = {\left(x + \frac{7}{2}\right)}^{2} + \left(\frac{48}{4} - \frac{49}{4}\right)$

$\rightarrow y = {\left(x - \left(- \frac{7}{2}\right)\right)}^{2} + \left(- \frac{1}{4}\right)$

$\textcolor{w h i t e}{\text{XXXXXX}}$which is the vertex form with the vertex at $\left(- \frac{7}{2} , - \frac{1}{4}\right)$