Quadratic Functions on Parameter Plane
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This example demonstrates the changes of quadratic functions on a parameter plane. Key mathematical concepts include the properties and graphs of quadratic functions. Using GeoGebra commands such as Point and If, you can dynamically adjust parameters and observe the changes in the graph of quadratic functions. Suitable for high school mathematics education and learning about quadratic function properties.
GeoGebra Commands & Parameters
Point(yAxis) → GPoint(xAxis) → FIf(d2 ≥ 0, sqrt(d2), sqrt((-d2))) → dPoint(h) → H
AI Drawing Prompt Reference
Draw a quadratic function graph on a parameter plane and observe how the graph changes by adjusting parameters. Start by taking a point G on the y-axis and a point F on the x-axis. Then, based on the value of d2, calculate the value of d: if d2 is greater than or equal to 0, d equals the square root of d2; otherwise, d equals the square root of the negative value of d2. Finally, take a point H at the calculated value of d.
The prompt above was compiled from the original drawing commands and is for reference only.