Exploring Polynomial Root Multiplicity

This GeoGebra interactive demonstrates how varying the multiplicity of polynomial roots affects the graph's behavior at the x-axis. When multiple factors share the same root, the curve transitions between crossing and tangentially touching the axis, illustrating the relationship between root multiplicity and graph behavior. The construction uses six GeoGebra objects (a–f), typically representing roots or coefficients via sliders, enabling real-time parameter adjustment. It is suitable for high school algebra and pre-calculus courses, as well as introductory calculus discussions on derivatives and tangent properties. Key concepts include polynomial functions, root multiplicity, graph transformations, and dynamic slider interaction.