# What is the vertex form of y= x(x - 7) ?

Mar 14, 2016

$y = 1 {\left(x - \frac{7}{2}\right)}^{2} + \left(- \frac{49}{4}\right)$

#### Explanation:

The general vertex form is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$ with vertex at $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

Given
$\textcolor{w h i t e}{\text{XXX}} y = x \left(x - 7\right)$

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

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

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

$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{1} {\left(x - \textcolor{red}{\frac{7}{2}}\right)}^{2} + \left(\textcolor{b l u e}{- \frac{49}{4}}\right)$