Family of Quadratic Curves
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This example demonstrates how changing parameters k, c, d affects the family of quadratic curves. Core math concepts include quadratic functions, parametric equations, and function graph transformations. GeoGebra objects k, c, d are used to control transformations like translation and scaling. Suitable for high school mathematics teaching to understand geometric transformations of quadratic function graphs.
GeoGebra Commands & Parameters
Numeric k(3.1)y = x^(2) - (2 * x) + ky = x^(2) + (k * x) + 1
AI Drawing Prompt Reference
Graph a parabola y=x^2-2x+k where k is a parameter, showing the change in the parabola as k varies, and then graph another parabola y=x^2+kx+1, also showing its change with parameter k, to demonstrate the effect of k on the position of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.