Parabola Shifter: Dynamic Exploration of Quadratic Parameters
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① This example uses sliders to dynamically adjust the parameters a, h, and k in the quadratic function y = a(x - h)² + k, visually demonstrating translations and scaling of the parabola on the coordinate plane. ② Core mathematical concepts include the vertex form of a quadratic function, vertex coordinates (h, k), direction and width of opening (determined by a), and transformations of function graphs. ③ Construction highlights: GeoGebra sliders a, h, k are created, the function f(x) = a*(x - h)^2 + k is defined, and a text object text1 displays the current function expression and vertex coordinates in real time, making parameter effects observable. ④ Suitable for middle and high school students learning properties of quadratic functions, as well as for teacher demonstrations or student self-exploration to understand the relationship between parameters and graph behavior.
GeoGebra Commands & Parameters
Numeric a(1)Numeric k(0)Numeric h(0)y = (a * (x + k)^(2)) + h
AI Drawing Prompt Reference
Draw a parabola y = a(x - h)² + k with its vertex at (h, k), where a, h, and k are adjustable sliders. First, create three sliders a, h, and k to represent the scaling, horizontal shift, and vertical shift of the parabola. Then define the function f(x) = a*(x - h)^2 + k and display the current function expression and vertex coordinates in real time.
The prompt above was compiled from the original drawing commands and is for reference only.