# How do you write the vertex form equation of the parabola y= -2x^2 + 12x - 13?

##### 1 Answer
May 12, 2017

$y = - 2 {\left(x - 3\right)}^{2} + 5$

#### Explanation:

$y = - 2 {x}^{2} + 12 x - 13$
x-coordinate of vertex:
$x = - \frac{b}{2 a} = - \frac{12}{-} 4 = 3$
y-coordinate of vertex:
$y \left(3\right) = - 2 \left(9\right) + 12 \left(3\right) - 13 = 18 - 13 = 5$
Vertex form:
$y = - 2 {\left(x - 3\right)}^{2} + 5$

Check:
Develop the vertex form:
$y = - 2 \left({x}^{2} - 6 x + 9\right) + 5 = - 2 {x}^{2} + 12 x - 13.$ OK