Write the Equation of the Parabola

① This example demonstrates how to write the equation of a parabola based on given geometric objects (points A, B, and a curve f), helping learners intuitively grasp the correspondence between the parabola's equation and its graph. ② Core mathematical concepts include the definition of a parabola (set of points equidistant from a fixed point and a fixed line), standard forms (e.g., y²=2px or x²=2py), focus and directrix, and determining equation parameters from given points. ③ Construction highlights: from the construction summary, the example uses GeoGebra objects point A, point B, and curve f, likely allowing users to drag points or adjust the curve to observe equation changes and derive the specific parabola equation. ④ Suitable for high school analytic geometry students or teachers for classroom demonstration, and for self-study to reinforce the link between parabola equations and graphs, enhancing visual-mathematical reasoning.