Approximating Gradient of a Parabola

① This GeoGebra example dynamically demonstrates how to approximate the slope of a tangent line to a parabola at a point using a secant line, visualizing the geometric meaning of the derivative. ② Core mathematical concepts include parabolas, secant slope, tangent slope, derivative definition, and the limit concept, integrating function graphing and coordinate geometry. ③ Construction details: Point creates points A and B on the parabola, Segment connects them to form a secant, OrthogonalLine constructs a perpendicular line through A (indicating tangent direction), Intersect finds intersection points, and rise/run are used to compute the slope. Dragging point B or using a slider changes the secant, showing the slope approaching the tangent slope. ④ Suitable for high school or introductory college calculus students to grasp the geometric intuition of derivatives, and useful for classroom demonstrations or self-study.