# What is the vertex form of 2y=(3x -3)(x - 5) ?

Jan 27, 2016

$y = \frac{3}{2} {\left(x - 3\right)}^{2} + \left(- 6\right)$ with vertex at $\left(3 , - 6\right)$

#### Explanation:

The vertex form of a parabola is
$\textcolor{w h i t e}{\text{XXX}} y = m {\left(x - a\right)}^{2} + b$
for a parabola with center at $\left(a , b\right)$

$2 y = \left(3 x - 3\right) \left(x - 5\right)$

$\rightarrow 2 y = 3 \left(x - 1\right) \left(x - 5\right)$

$\rightarrow \frac{2}{3} y = {x}^{2} - 6 x + 5$

$\rightarrow \frac{2}{3} y = \left({x}^{2} - 6 x + 9\right) + 5 \left(- 9\right)$

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

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

$\rightarrow y = \frac{3}{2} {\left(x - 3\right)}^{2} + \left(- 6\right)$

graph{((3x-3)(x-5))/2 [-1.27, 9.823, -7.815, -2.266]}