Tangent Lines to Parabolas

①This example demonstrates how to construct tangent lines to a parabola in GeoGebra and dynamically observe the slope of the tangent at a moving point. ②Core mathematical concepts include the definition of a tangent to a parabola, the geometric meaning of the derivative, the relationship between slope and the point of tangency, and the uniqueness of the tangent at a given point. ③Construction details: using the Point command to place a point on the parabola, the Tangent command to generate the tangent line at that point, and the Slope command to compute and display the slope; key objects include the parabola f, point A, tangent lines m, m_1, m_2, and slope values a, b, c, d. ④This is suitable for high school or early college students learning the geometric interpretation of derivatives, tangent line equations, and exploring how the slope changes as the point moves along the curve, serving as an interactive visual aid for introductory calculus.