Open Middle: Parabola Equation (2) Modeling Exercise

This example uses an “open middle” task to help learners investigate how a parabola’s graph and equation form change under given constraints. It centers on conic sections—specifically parabolas—linking the geometry of a parabola with algebraic representations such as quadratic function form and parameter-based equation setup. The construction highlights conditional logic (If) for switching behaviors, interactive mode control (Mode), and dynamic input/feedback using Textfield, InputBox, and button1 to trigger updates. Key GeoGebra components include equation objects (eq1, eq2) and multiple parameter/intermediate variables (e.g., a, b, h, k, c, d, f, g and points like P, Q, A, B) that drive the dynamic construction. It is well suited for middle/high school or early undergraduate instruction in coordinate geometry, function graphing, and guided modeling with sliders and algebraic condition checking.