Quadratic Functions in Vertex Form by Dennis Weber
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This example demonstrates the graph of a quadratic function in vertex form y=a(x-h)^2+k, showing how parameters a, h, and k affect the graph. Key math concepts include quadratic functions, vertex form, translations, and伸缩 transformations. Constructed using GeoGebra sliders for h, k, and a to visualize the changes. Suitable for high school mathematics education to understand the properties of quadratic function graphs and the meaning of parameters.
GeoGebra Commands & Parameters
Numeric h(0)Numeric k(0)Numeric a(1)g(x) = x^(2)f(x) = (a * (x - h)^(2)) + k
AI Drawing Prompt Reference
Draw the graph of a quadratic function in vertex form, y = a(x − h)^2 + k. Create three adjustable parameters: h for horizontal shift, k for vertical shift, and a for scaling. Use a coordinate plane as the background. Show a reference parabola g(x) = x^2, and then plot the main function f(x) = a(x − h)^2 + k. Allow the viewer to change h, k, and a (via numeric sliders) to observe how the parabola translates and scales.
The prompt above was compiled from the original drawing commands and is for reference only.