**How Will This Worksheet on "Solve Quadratic Inequalities" Benefit Your Student's Learning?**

- Reinforces understanding of quadratic inequalities and their solutions.
- Develops critical thinking and analytical skills through problem-solving.
- Strengthens algebraic proficiency in manipulating quadratic expressions.
- Enhances graphical interpretation of quadratic inequalities on number lines or coordinate planes.
- Applies math concepts to real-world scenarios through inequality modeling.
- Promotes logical reasoning in interpreting and evaluating quadratic inequality solutions.
- Prepares students for assessments with quadratic inequality-solving components.
- Encourages self-directed learning and builds confidence in problem-solving abilities.

**How to Solve Quadratic Inequalities?**

- Ensure the quadratic inequality is in the form \( ax^2 + bx + c \, (<, \leq, >, \geq) \, 0 \).
- Solve the equation \( ax^2 + bx + c = 0 \) to find the critical points. These roots (`x`-values) divide the number line into intervals.
- Choose a test point from each interval between and beyond the roots.
- Substitute these test points into the quadratic expression \( ax^2 + bx + c \) to determine if the expression is positive or negative in that interval.
- Based on the sign in each interval and the inequality sign ( \(<, \leq, >, \geq\) ), determine which intervals satisfy the inequality.
- Include or exclude the roots based on whether the inequality is strict (\(<,>\)) or non-strict (\(\leq, \geq\)).
- Write the solution as an interval or a union of intervals.