Parabola with Tangent, Boxplot, and Binomial Distribution

This GeoGebra example dynamically demonstrates the parabola and its properties while integrating tangent lines, boxplots, statistics, and binomial distribution. The core concept is the quadratic function in vertex form y=a(x-h)^2+k, where parameters a, h, k control the opening, width, and vertex position. The tangent line at a point on the parabola is constructed, illustrating the derivative and slope. Construction uses sliders or input boxes for parameters a, h, k, and auxiliary objects c, d, b to define the tangent and related geometric elements. Additionally, a boxplot visualizes data distribution, and a binomial distribution function is included for probability statistics. Suitable for high school and early college students to explore quadratic transformations, tangent geometry, and statistical visualization in an integrated manner, serving as a cross-topic teaching resource.