# What is the vertex form of y=-1/3(x-3)(x/3+7) ?

Dec 15, 2017

Vertex form of equation is $y = - \frac{1}{9} {\left(x + 9\right)}^{2} + 16$ and vertex is $\left(- 9 , 16\right)$

#### Explanation:

Vertex form of equation is $y = a {\left(x - h\right)}^{2} + k$, whose vertex is $\left(h , k\right)$. Hence

$y = - \frac{1}{3} \left(x - 3\right) \left(\frac{x}{3} + 7\right)$

= $- \frac{1}{9} \left(x - 3\right) \left(x + 21\right)$

= $- \frac{1}{9} \left({x}^{2} - 3 x + 21 x - 63\right)$

= $- \frac{1}{9} \left({x}^{2} + 18 x + 81 - 81 - 63\right)$

= $- \frac{1}{9} \left({\left(x + 9\right)}^{2} - 144\right)$

= $- \frac{1}{9} {\left(x + 9\right)}^{2} + 16$

and vertex is $\left(- 9 , 16\right)$

graph{ -1/9(x+9)^2+16 [-19, 1, 8, 18]}