Graphical Solutions of Quadratic Inequalities

This GeoGebra example visualizes how the solution set of a quadratic inequality changes by showing the relevant regions on the graph. It focuses on key ideas such as quadratic (parabola) behavior, roots (x-intercepts), vertex/opening direction, and determining where an inequality holds by comparing the parabola with reference lines (e.g., the x-axis) to obtain interval-based solution sets. The construction leverages GeoGebra commands and objects mentioned in the summary: Root to compute and mark the zeros, Point/Segment to define critical points and interval endpoints, and Vector (and auxiliary objects) for direction/annotation support. It also uses graphing and visualization elements (e.g., graph, trace) along with interactive controls (button*) and text labels (text*) to guide the viewer from the computed roots to the plotted solution region. Suitable for secondary school and early college learning on inequalities and quadratic functions.