# How do you write  y =2x^2 - 5x - 6 in vertex form?

Jul 14, 2016

$y = 2 {\left(x - \frac{5}{4}\right)}^{2} - \frac{73}{8}$

#### Explanation:

$y = 2 {x}^{2} - 5 x - 6$
x-coordinate of vertex:
$x = - \frac{b}{2 a} = \frac{5}{4}$
y-coordinate of vertex:
$y \left(\frac{5}{4}\right) = 2 \left(\frac{25}{16}\right) - 5 \left(\frac{5}{4}\right) - 6 = - \frac{25}{8} - \frac{48}{8} = - \frac{73}{8}$
Vertex $\left(\frac{5}{4} , - \frac{73}{8}\right)$
Vertex form of y:
$y = 2 {\left(x - \frac{5}{4}\right)}^{2} - \frac{73}{8}$
graph{2x^2 - 5x - 6 [-20, 20, -10, 10]}