Dynamic Exploration of Quartic Polynomial Roots and Graphs

This GeoGebra example demonstrates the roots of a quartic (fourth-degree) polynomial function and their graphical representation on the coordinate plane, allowing dynamic observation of real and complex roots. The core mathematical concepts include polynomial roots, power functions, function graphing, algebraic equation solving, and the distribution of roots in the complex plane. The construction uses GeoGebra Textfield and LaTeX input boxes (inputBox1 through inputBox4) to control the leading coefficient a and polynomial terms, generating the function f and its four roots root_1 to root_4. The roots are plotted as points A, B, C, D, with text objects text2, text3, and text4 displaying their numerical values. This interactive visualization is suitable for high school algebra and functions instruction, as well as pre-calculus or undergraduate courses focusing on polynomial root visualization and classroom demonstration.