# How do you graph the inequality y>x^2-36?

Nov 24, 2017

See Below.

#### Explanation:

First graph $y = {x}^{2} - 36$ Remember to use a dashed line because this is not an equal to inequality, and the line will not be an included region.

Notice that this is the graph of $y = {x}^{2}$ translated 36 units in the negative $y$ direction. Find the roots to the equation. This will then give you 3 points to plot.

Roots:

${x}^{2} - 36 = 0 \implies {x}^{2} = 36 \implies x = \pm 6$

Roots: $x = 6 \mathmr{and} x = - 6$

From the graph take an $x$ value and a $y$ value inside and outside of the parabola and test them in the inequality:

$y > {x}^{2} - 36$

From outside the parabola:

$x = 10 , y = 10$

$10 > {\left(10\right)}^{2} - 36$

$10 > 64$

This is False, so included region is inside the parabola.

Graph:

graph{y > (x^2-36) [-74.04, 74.07, -37, 37.04]}