Parabola and Circle Intersection – Dynamic Exploration with GeoGebra Slider

① This example dynamically visualizes the intersection changes between the parabola y = a(x + 1)(x − k) and the unit circle x² + y² = 1. ② Core mathematical concepts covered include quadratic function graphs, circle equations, coordinate geometry intersection problems, the effect of parameters a and k on graph positions, and dynamic geometry demonstrations using a slider. ③ The GeoGebra construction employs the Intersect, Circle, Midpoint, Line, and Segment commands. Key objects are O (circle center), c (circle), P (intersection), k (parameter point), m (midpoint), b (auxiliary point), Q (another intersection), a (parameter a), e, F, f, V, d, g, h, etc., enabling real‑time updates via a slider. ④ Suitable for high‑school mathematics (analytic geometry, problem solving) and college introductory mathematics courses, especially for teaching the combined application of quadratic functions and circles, parameter variation studies, and practical exploration of dynamic geometry software.