Question

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

Answer 1

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=>x^2=36=>x=+-6`

Roots: `x = 6 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 > (10)^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]}