This week in Precalc 11 I learned about graphing linear and quadratic inequalities.

First, linear and quadratic inequalities keep the same shape as equations, as they still include the base and $y=x^2$ however, the way to indicate them is different.

If the inequality has or , the line of the inequality will be solid, but if it’s only or , then it must be a dotted line.

Additionally, you shade in the side of the line or parabola that has the solutions. An easy way to figure out which side works is to use the test point . The reason this is usable is because 0,0 is not only a simple point to find, but by plugging it in to the equation, you can figure out if the side that includes 0,0 satisfies it or not. If the equation makes sense when using the point 0,0, then the side you shade is the one with 0,0. If not, then you shade the other side.

For example, if you have the inequality , then putting in will make it , which satisfies the equation, meaning you shade that side.

The same goes for a parabola, if you were to have the inequality , you’ll be able to test it with zero as well.

Using these rules and tricks for graphing, you can put any inequality on to a graph.