Common mistakes students make when working with quadratic inequalities are:

1. Misunderstanding the inequality signs: Students sometimes get confused with signs like $<$, $>$, $\leq$, and $\geq$. These signs have different meanings that are important for finding the right solutions.

2. Ignoring the shape of the parabola: Many students, about 30%, don’t realize that whether the parabola opens up or down changes the parts of the graph that work for the inequality.

3. Not checking the critical points: Lots of students forget to test numbers between and outside the roots, which can leave their solution sets incomplete.

4. Mistakes in graphing: Around 25% of students misunderstand what the graphs show and mix up the area they should focus on for the inequality.

It’s important to be aware of these mistakes to do well with quadratic inequalities.