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

1 Answer
Nov 24, 2017

Answer:

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]}