# How do you write y =-2x^2 + 12x - 13 in vertex form and identify the vertex?

May 24, 2015

The vertex form is:

$y - {y}_{v} = a {\left(x - {x}_{v}\right)}^{2}$.

So:

$y = - 2 \left({x}^{2} - 6 x\right) - 13 \Rightarrow$

$y = - 2 \left({x}^{2} - 6 x + 9 - 9\right) - 13 \Rightarrow$

$y = - 2 \left({x}^{2} - 6 x + 9\right) + 18 - 13 \Rightarrow y = - 2 {\left(x - 3\right)}^{2} + 5 \Rightarrow$

$y - 5 = - 2 {\left(x - 3\right)}^{2}$, and the vertex is $V \left(3 , 5\right)$.