Solving Quadratic Equations via Graphs: Parabola–Root Connection

This example demonstrates how to solve quadratic equations by linking algebraic roots to the graphical behavior of a parabola in the coordinate plane. It highlights the relationship between a quadratic equation and its corresponding quadratic function, showing that the solutions are represented by key points such as the intercepts (roots) x1 and x2. The construction uses LaTeX text objects (text1, text2, text3, text4) to display the mathematical expressions clearly, while parameters a, b, c and derived expressions (f, g, eq2, d, e, h) generate the quadratic equation/function being studied. The setup is designed to make the equation’s solution(s) visually accessible and to support discussion of how changing coefficients affects the roots and the graph. Suitable for middle and high school math learning, especially when teaching the “functions and equations” connection, graph-based reasoning, and quadratic solving strategies.