Question

How do you graph the inequality `y<x^2-16`?

Answer 1

See below.

Explanation:

Graph `y = x^2 - 16`

This will give you the boundary of the regions. Remember to use a dashed line as this is a less than and not a less than or equal to inequality, so the curve will not be an included region.

Test for a coordinate inside the parabola and outside the parabola.

Inside parabola:

`( 0 ,5)`

`5 < 0^2-16`

FALSE

Outside parabola:

`(10 ,5)`

`5 < 10^2 -16 => 5< 84`

TRUE

Shaded area is outside parabola:

graph{y < x^2-16 [-36.53, 36.57, -18.25, 18.27]}