# What is the vertex form of 3y=-2(x+3)(x-1) ?

${\left(x - - 1\right)}^{2} = - \frac{3}{2} \left(y - \frac{8}{3}\right)$

#### Explanation:

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

divide both sides of the equation by -2

$\frac{3 y}{- 2} = \frac{- 2 \left(x + 3\right) \left(x - 1\right)}{- 2}$

$\frac{3 y}{- 2} = \frac{\cancel{- 2} \left(x + 3\right) \left(x - 1\right)}{\cancel{- 2}}$

$\frac{3 y}{- 2} = \left(x + 3\right) \left(x - 1\right)$

Expand the right sides of the equation by multiplication

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

complete the square

$- \frac{3}{2} y = {x}^{2} + 2 x + 1 - 1 - 3$

$- \frac{3}{2} y = {\left(x + 1\right)}^{2} - 1 - 3$

$- \frac{3}{2} y = {\left(x + 1\right)}^{2} - 4$

transpose the -4 to the left side

$- \frac{3}{2} y + 4 = {\left(x + 1\right)}^{2}$

factor out the -3/2 so that coefficient of y is 1 inside the grouping symbol

$- \frac{3}{2} \left(y - \frac{8}{3}\right) = {\left(x - - 1\right)}^{2} \text{ " }$this is now the vertex form

God bless....I hope the explanation is useful.