Quadratic Root Graph Transformation 2

This example demonstrates how the graph of a quadratic function transforms when its roots (zeros) change, visually showing the relationship between roots and graph position. Core mathematical concepts include roots of quadratic functions, factorization, graph translation and scaling, and the arithmetic mean relationship between roots. Construction: using GeoGebra objects f and g, where f is the original quadratic and g is a transformed version, sliders or dynamic parameters control root positions to observe the graph's dynamic response. Suitable for high school students learning quadratic function properties, graph transformations, and zero-point problems, as well as for teacher demonstrations to build intuitive connections between algebraic expressions and geometric graphs.