Build & Fit: Quadratic Functions and Their Derivatives

① This interactive GeoGebra example demonstrates how to construct and fit a quadratic function, simultaneously displaying its derivative line and tangent behavior, allowing users to explore how the parabola changes with parameter adjustments. ② Core mathematical concepts include quadratic functions, derivatives as slopes of tangents, polynomial fitting, intersections, extrema, and the use of vectors for geometric representation. ③ Construction highlights: using GeoGebra commands such as Polynomial to define the quadratic, Intersect to find key points, and Derivative to generate the derivative function; objects include functions f and g, points A, B, C, D, E, lines L and Q, and multiple text labels (text1–text13) that dynamically display coordinates and slope values. ④ Suitable for high school or introductory college courses on functions and calculus, this example helps students visualize the relationship between a quadratic curve and its linear derivative, and understand how coefficients affect the graph and tangent slopes.