# What is the vertex form of  3y = - 3x^2 + 12x + 7 ?

${\left(x - 2\right)}^{2} = - \left(y - \frac{19}{3}\right)$

#### Explanation:

$3 y = - 3 {x}^{2} + 12 x + 7$

$3 y = - 3 \left({x}^{2} - 4 x\right) + 7$

$3 y = - 3 \left({x}^{2} - 4 x + 4\right) + 12 + 7$

$3 y = - 3 {\left(x - 2\right)}^{2} + 19$

$y = - {\left(x - 2\right)}^{2} + \frac{19}{3}$

${\left(x - 2\right)}^{2} = - \left(y - \frac{19}{3}\right)$

Above is the vertex form of parabola which represents a downward parabola with the vertex at

$\left(x - 2 = 0 , y - \frac{19}{3} = 0\right) \setminus \equiv \left(2 , \frac{19}{3}\right)$