Turning Points and Intercepts of a Parabola Function

This GeoGebra example dynamically demonstrates how to find the turning point (vertex) and intercepts of a parabola function, visually highlighting key features of quadratic graphs. Core mathematical concepts include the vertex formula, discriminant and roots, intersection points with axes, and the geometric meaning of extrema. Construction details: commands such as If, Extremum, and Intersect are used to compute critical points and intersections; Textfield and InputBox1 enable interactive user input for answers; LaTeX displays mathematical expressions; Segment connects relevant points for clarity. Suitable for middle and high school students learning quadratic functions, graph analysis, and the connection between algebra and geometry, as well as for classroom demonstrations or self-paced exploration.