Graphical Representation of Quadratic Polynomial

This GeoGebra example dynamically illustrates the graph of a quadratic polynomial y = ax² + bx + c, showing the parabolic shape, vertex, x-intercepts, and how changing coefficients affects the curve. Core mathematical concepts include quadratic functions, symmetry of parabolas, discriminant and root relationships, and similarity transformations (translation and scaling). Construction details: the Intersect command finds intersections with axes, Sum computes function values, Name labels objects, and TableText generates data tables; objects include coefficients a, b, c, function f, points A and B, and auxiliary points (A3-A10, B2-B10, C2-C10, D2-D10) to display variations under different coefficient sets. Suitable for middle and high school mathematics, this resource helps students intuitively grasp properties of quadratic functions, graph transformations, and the algebra-geometry connection, and is ideal for classroom demonstrations or exploratory learning.