This week we looked at inequalities. We mainly focused on graphing true statements with linear and quadratic inequalities.

Graphing Linear Inequalities:

First you start off with a linear inequality, for example:

As you can see this is in the form of y = mx + b so it is indeed linear.

Then you graph the line:

Now we need to shade a side of the line to represent all of the possible answers in the inequality.

In order to do so we must choose a “test point” and see if it makes the inequality a true statement or not.

I am going to choose the test point of (0,0):

This is not a true statement so we will shade the other side of the line:

It is shown as a dotted line since all of the points on the line are not included as answers to the inequality.

Graphing Quadratic Inequalities:

The same rules apply when graphing quadratic inequalities.

Here is a quadratic inequality:

You can tell the scale factor is the regular 1,3,5 pattern and the y-intercept is 5 so you can graph this:

Then pick a test point, i will choose (0,0) again:

This is a true statement so we will shade the area outside of the parabola: