Dynamic Exploration of a Vertical Parabola

① This GeoGebra example dynamically demonstrates the geometric construction of a vertical parabola, including its focus, directrix, vertex, axis of symmetry, and latus rectum, while displaying both standard and general equations in real time. ② Core mathematical concepts include the definition of a parabola as the locus of points equidistant from a fixed point (focus) and a fixed line (directrix), the relationship between focus and directrix, vertex coordinates, axis of symmetry equation, latus rectum length, and the connection between quadratic functions and conic sections. ③ Construction highlights: using GeoGebra commands such as Segment, Line, Parabola, Point, OrthogonalLine, and Intersect, the example builds objects like focus F, directrix d, vertex v, axis of symmetry aos, and sliders (chkSliders) to control parameters; a button (btnGo) triggers animation, checkboxes (chkForm) switch equation forms, and dynamic text displays equations and geometric quantities. ④ Suitable for high school analytic geometry or pre-calculus courses, this resource aids teachers in classroom demonstrations and students in exploring how parameter changes affect the parabola's shape and position.