# What is the vertex form of y= x^2 + 7x – 6 ?

Aug 31, 2017

y=color(green)1(x-color(red)(""(-7/2)))^2+color(blue)(""(-25/4))
with vertex at
$\textcolor{w h i t e}{\text{XXX}} \left(\textcolor{red}{- \frac{7}{2}} , \textcolor{b l u e}{- \frac{25}{4}}\right)$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} + 7 x + 6$

Complete the square:
$\textcolor{w h i t e}{\text{XXX")y=x^2+7xcolor(magenta)(} + {\left(\frac{7}{2}\right)}^{2}} + 6 \textcolor{m a \ge n t a}{- {\left(\frac{7}{2}\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} y = {\left(x + \frac{7}{2}\right)}^{2} + \frac{24}{4} - \frac{49}{4}$

$\textcolor{w h i t e}{\text{XXX}} y = {\left(x + \frac{7}{2}\right)}^{2} - \frac{25}{4}$

Some instructors might accept this as a solution,
but in its complete form, the vertex form should look like:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$
in order to easily read the vertex coordinates.

You should have no difficulty in converting to the form provided in the "Answer".
$\textcolor{g r e e n}{m}$ must be $\textcolor{g r e e n}{1}$
converting $\left(x + \frac{7}{2}\right)$ gives (x-color(red)(""(-7/2)))
and $- \frac{25}{4}$ is equivalent to $\textcolor{b l u e}{+ \left(- \frac{25}{4}\right)}$