Parabolas and Vertex Form
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This example demonstrates parabolas and their vertex form. It involves the vertex form of a quadratic function, adjusting parameters a, h, and k to change the shape, position, and direction of the parabola. The GeoGebra commands used include a, h, k, g, f, text2, text1, A, b, text3, and text4. Suitable for high school mathematics education and learning about quadratic functions.
GeoGebra Commands & Parameters
Numeric a(1.0)Numeric h(0.0)Numeric k(0.0)g(x) = x^(2)f(x) = (a * (x - h)^(2)) + k(h, k)x = h
AI Drawing Prompt Reference
Draw a coordinate plane with a basic upward-opening parabola whose vertex is at the origin. Then introduce three adjustable parameters that control the parabola's width, horizontal shift, and vertical shift. Based on these, draw a transformed parabola with its vertex located at the shifted coordinates. Add a vertical dashed line through this vertex as the axis of symmetry. Label the vertex coordinates and the axis equation, and keep the original parabola for comparison. The figure should clearly show how changing the parameters affects the parabola's shape and position.
The prompt above was compiled from the original drawing commands and is for reference only.