# How do you graph y>=2x^2-2x-5?

Jan 1, 2017

The graph is inserted.

#### Explanation:

graph{y>=2x^2-2x-5 [-6, 6, -12, 12]}

$y = 2 {x}^{2} - 2 x - 5 = 2 {\left(x - \frac{1}{2}\right)}^{2} - \frac{11}{2}$, giving the standard form

${\left(x - \frac{1}{2}\right)}^{2} = 4 \left(\frac{1}{8}\right) \left(y + \frac{11}{2}\right)$

The vertex ( least-y point ) of this parabola is $\left(\frac{1}{2} , - \frac{11}{2}\right)$.

For any point (x, y) on or above this parabola,

y >= 2x^2-2x-5>=-11/2#.