Quadratic Function Coefficient Alpha Demo
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Quadratic functions
This example demonstrates the effect of coefficient alpha in the quadratic function y=ax²+bx+c on the direction and width of the function graph. Core math concepts include quadratic functions, coefficients, function graph transformations, and analytical geometry. GeoGebra commands/objects used: alpha (coefficient), c (constant term), A (point), b (coefficient). Suitable for high school students to learn and understand the properties of quadratic functions, and can be used in function graph transformation teaching.
GeoGebra Commands & Parameters
Numeric α(-1.0)y = (x + α)^(2)((-α), 0)x = (-α)
AI Drawing Prompt Reference
Draw the graph of the quadratic function y=(x+α)^2 where α is a variable parameter, showing its changes in direction and width. Also mark the point (-α, 0) and the vertical line x=-α, displaying their relationship with the function graph to demonstrate the effect of coefficient α on the quadratic function.
The prompt above was compiled from the original drawing commands and is for reference only.