Graphing quadratic inequalities is honestly pretty easy to get down as long as you understand quadratic equations and basic graphing, two things we’ve learned before this unit. The trick is just understanding how the two work together and more importantly, why they work together. Here are a few steps:
- Graph the Quadratic Function:
Start by plotting the quadratic function without even looking at the inequality symbol, that won’t be important until later on. I won’t go over how to graph a quadratic function as I’ve already done that in a previous blog post, but the final result should be a parabola.
2. Find the Shaded Area:
My basic rule of thumb for understanding which inequality will correlate to which region being shaded is simply that less means under and more means over. This works best for me when I visualize it like a linear inequality. I know that anything above the line will be greater than / greater than or equal to that line- the same going for less than / less than or equal to. Now if I imagine that a quadratic is a line simply being bent (which isn’t the full story but no need to overcomplicate right now), it’s super easy to still use that under/over method. If the parabola opens up, the under is the space outside the parabola, and if it reflects down, it’s the space inside, and vise versa for the over.
*It’s important to remember that when it’s “less/greater than or equal to” the line on the graph will be solid, but if it excludes the line, the line will instead be dotted/broken.
3. Test a pointÂ
Finally, it’s good to make a test point on the graph, the simplest being (0, 0). If you can plug it into the inequality, and get a true answer, then you know that’s the space that needs to be shaded. If not, it needs to be empty.