Repeated Roots Graph Guess Formula

This interactive GeoGebra example demonstrates how repeated roots (e.g., double or triple roots) of a polynomial affect its graph, and challenges users to guess the algebraic formula based on visual features. The core mathematical concepts include polynomial roots, multiplicity, factorization, and the correspondence between equations and graphs. Construction: only a single function object f is defined; by editing its expression (e.g., f(x)=(x-a)^n(x-b)), users observe whether the curve touches or crosses the x-axis at the root, revealing the role of multiplicity. Suitable for high school and college students studying functions, equations, and polynomial properties, as well as a visual introduction to derivatives and extrema in precalculus or calculus. Sliders or input boxes allow real-time parameter changes, reinforcing the link between algebraic form and graphical behavior.