Quadratic Equation Graph with Geometric Construction

①This example illustrates the graph of a quadratic equation and its interplay with geometric elements like perpendicular lines, intersection points, and extrema, demonstrating how algebraic equations correspond to visual graphs. ②Core mathematical concepts include quadratic equations, quadratic function graphs, vertex (extremum), roots (zeros), orthogonal lines, and intersection points, while also touching on hypothesis testing, parallelograms, similar triangles, median values, and pie charts as broader contexts. ③Construction details: from the summary, GeoGebra commands such as Extremum, OrthogonalLine, Root, Point, Segment, and Intersect are used, with objects including coefficients a, b, c, function f, points A, B, C, D, E, lines g, h, i, j, k, text label text1, and segments d, e. ④This is suitable for middle and high school mathematics education, helping students understand properties of quadratic functions, the relationship between roots and extrema, and dynamic exploration combining algebra and geometry.