Vertical Stretch Effect of Parameter a in Quadratic Functions
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① This example dynamically demonstrates how changing the parameter a in a quadratic function y=a(x-h)²+k affects the vertical stretch or compression of its parabolic graph, including the direction of the opening. ② The core mathematical concept is the role of the leading coefficient a in quadratic functions, illustrating vertical transformations (stretching, compressing, and reflection) and how it alters the shape of the parabola. ③ Construction details: The GeoGebra commands include Vertex to define the vertex, and sliders a, h, k to control the function parameters; objects include text1-text6 for labeling the function expression and vertex coordinates, and points A, B, C, D, E for marking key points or auxiliary elements. The dynamic sliders drive real-time changes in the graph. ④ Suitable for middle school to high school students learning properties of quadratic functions, and useful for teachers in classroom demonstrations or for students' independent exploration of parameter effects, fostering a visual and intuitive understanding of algebraic concepts.
GeoGebra Commands & Parameters
Vertex(c) → C, , ,
AI Drawing Prompt Reference
Draw a parabola representing the quadratic function y=a(x-h)²+k, with three sliders labeled a, h, and k to control the parameters. Mark the vertex of the parabola with a point and display its coordinates. Include text labels showing the function expression and the vertex coordinates. As the slider a changes, the parabola should stretch or compress vertically, opening upward if a is positive and downward if a is negative. Add a few auxiliary points on the graph to help observe the shape changes. The overall image should clearly illustrate how the parameter a affects the vertical stretch and the direction of the parabola's opening.
The prompt above was compiled from the original drawing commands and is for reference only.