# What is the vertex form of y=-9x^2 +12x - 18 ?

Dec 26, 2015

Below is the proof (a completion of square)

#### Explanation:

$y = - 9 {x}^{2} + 12 x - 18$

$y = - 9 \left({x}^{2} - \frac{12}{9} x\right) - 18$

y = -9(x^2 - 12/9x + _ - _ ) - 18#

$_ = {\left(\frac{- \frac{12}{9}}{2}\right)}^{2}$

$_ = \frac{4}{9}$

$y = - 9 \left({x}^{2} - \frac{12}{9} x + \frac{4}{9}\right) - \frac{4}{9} \left(- 9\right) - 18$

$y = - 9 {\left(x - \frac{2}{3}\right)}^{2} - 14$

So, $y = - 9 {x}^{2} + 12 x - 18$ is equal to $y = - 9 {\left(x - \frac{2}{3}\right)}^{2} - 14$

Hopefully that explanation helped!