Miss Smith's Parabola Transformation

① This example dynamically demonstrates the transformation of the parabola y = a(x - h)² + k using sliders, showing how parameters a, h, and k affect the shape and position of the graph. ② Core mathematical concepts include the standard form of a quadratic function, vertex coordinates, axis of symmetry, direction and width of the opening, as well as horizontal and vertical translations and vertical scaling. ③ Construction highlights: based on the construction summary, objects f (the parabola function), h (horizontal shift), k (vertical shift), a (opening coefficient), and g (possibly an auxiliary graph or transformed function) are used, with sliders controlling these parameters to update the graph in real time. ④ Suitable for upper middle school to high school students learning quadratic function transformations, and for teachers to demonstrate in class, helping students build an intuitive connection between parameters and graph behavior.