This week in math we learned how to graph quadratic inequalities in two variables. Some basic information to know first is what the signs mean, e.g. < or > means there it will be a broken line when graphed (or dotted line). ≤ or ≥ means it will be a solid line when graphed.
The first step is to get y by itself on one side of the inequality if it isn’t already. Before doing this you may need to do some distribution. Once you have y by itself and the quadratic inequality is in general form (most likely), now you will have to convert into standard form (or vertex form). Recall how to do this from the previous chapter. Once it’s in vertex form, you know where the vertex is, the stretch or compression, and whether it opens up or down. This is enough to now graph it.
Once you’ve graphed the parabola, you know need to know which side of the graph to shade. To do this, you will choose a point on one side of the graph (inside the parabola or outside, but not on the line) and put it into the original equation to see if you get a true or false statement. Once you solve it, if it’s true then that means the side the point is on will be shaded, if it’s a false statement then it means the side the point ISN’T on will be shaded. I’ve included an example below to help you understand what this would look like visually.