How to Solve a System of Quadratic Inequalities by Graphing

The Organic Chemistry Tutor

This educational video provides a step-by-step tutorial on solving a system of quadratic inequalities through graphing. The narrator demonstrates how to find the solution set for a system containing two quadratic inequalities: y > x² - 4 and y ≤ -x² + 2x + 3. The video breaks down the process into manageable parts, starting with graphing each parabola individually by finding key features such as the vertex, x-intercepts, and y-intercepts. The tutorial emphasizes critical details that often confuse students, such as the distinction between dashed and solid boundary lines based on inequality symbols (greater than vs. less than or equal to). It also covers the logic behind shading specific regions (above vs. below the parabola) and identifies the final solution as the overlapping shaded area between the two curves. The use of color-coding helps visually distinguish between the two inequalities and their intersection. This resource is highly valuable for Algebra II and Pre-Calculus classrooms. It reinforces graphing skills for parabolas while introducing the logic of systems of inequalities. Teachers can use this video to model the procedural steps required to solve these problems or as a review tool for students struggling with the multi-step process of finding vertices, intercepts, and determining the correct shading regions.