Solving Quadratic Equations Graphically by Adding a Straight Line to a Quadratic

① This GeoGebra example demonstrates how to solve a quadratic equation graphically by adding a straight line to a quadratic function graph and finding their intersection points. ② The core mathematical concepts include quadratic equations, quadratic functions, linear equations, and the relationship between intersection points and equation roots: the x-coordinates of intersections of y=f(x) and y=g(x) are the solutions to f(x)=g(x). ③ Construction highlights: the applet uses commands such as Random, RandomElement, Remove, If, Simplify, Intersect, Extremum, Expand, and Factor to generate random coefficients and compute intersections and vertices. It includes interactive elements like buttons and sliders, with objects for the quadratic function, the line, intersection points, extrema, and adjustable coordinate ranges. ④ This resource is suitable for high school students (or advanced middle school) to explain or review the graphical method of solving quadratic equations, and can be used for classroom demonstration or self-paced exploration.