Projectile Range via Parabola Parameters: How Angle Changes Landing Distance

This example visualizes how a projectile’s range (landing distance) changes as the launch angle varies, linking geometric construction with function graphs. It centers on quadratic functions and parabolas, using trigonometric functions (sine/cosine) to relate angle parameters to model quantities, and on coordinate-geometry interpretation of curves and their key points. Construction-wise, GeoGebra uses Polygon to assemble the main geometric configuration and employs a set of parameter-dependent points and segments (e.g., V_0, a, b, t, P, A, B, C, M) to represent the relevant locations and boundaries of the projectile motion/range region. Multiple text labels (text1–text10) and interactive controls (button1–button4) support switching parameter values and comparing outcomes. Function-related objects (e.g., f, g, and parameters such as p, q, h with additional derived quantities d_1, e, f_1, g_1) connect the trigonometric/parameter setup to the resulting quadratic curve or graph features. Suitable for high school to early university lessons on quadratic modeling, trigonometric modeling, and interactive graphing/visual reasoning.