Graphical Solution of a Quadratic Inequality

This example demonstrates how to find and visualize the solution set of a quadratic inequality by using the graph of a quadratic function and its intersection/sign behavior on the coordinate plane. It centers on key ideas such as quadratic functions, computing roots (which determine the critical endpoints of the intervals), sign analysis of a parabola (based on the opening direction and whether the inequality is ≥ or ≤), and representing the corresponding solution intervals. From the construction summary, the model is built with Root to generate the roots (e.g., objects like o1–o5), Point and Segment to place and connect key boundary points (objects such as a, b, c, d and related labeled points), and Vector for supporting geometric/annotation direction elements. A graphical function/graph layer (e.g., graph, f) together with text labels and interactive controls (buttons) highlights the region satisfying the inequality, often using trace to show the evolving solution visualization. Suitable for middle to high school math instruction, especially teaching the interval-based solution method using graphing.