# What is the vertex form of y=x(x-3) ?

May 7, 2016

$y = {\left(x - \frac{3}{2}\right)}^{2} - \frac{9}{4}$

#### Explanation:

$y = x \left(x - 3\right)$ $\Rightarrow y = {x}^{2} - 3 x$

Use the process of completing the square.

$y = {x}^{2} - 3 x + {\left(\frac{3}{2}\right)}^{2} - {\left(\frac{3}{2}\right)}^{2}$

Note in the previous line $+ {\left(\frac{3}{2}\right)}^{2} - {\left(\frac{3}{2}\right)}^{2} = 0$, so the value of the expression has not changed.

$y = {\left(x - \frac{3}{2}\right)}^{2} - \frac{9}{4}$