Quadratic Functions - Vertex Form
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This example demonstrates the graph of a quadratic function in vertex form f=a(x-h)^2+k, showing how parameters a, h, k affect the parabola's shape and position. Key math concepts include quadratic functions, vertex form, and parameter transformations. GeoGebra commands used are objects f, a, h, k, g, with sliders for interactive exploration. Suitable for high school mathematics education to understand the properties of quadratic function graphs and the application of vertex form.
GeoGebra Commands & Parameters
y = x^(2)Numeric a(1)Numeric h(0)Numeric k(0)y = (a * (x - h)^(2)) + k
AI Drawing Prompt Reference
Draw the basic parabola y = x² on a coordinate plane, then add three sliders for parameters a, h, and k to display the vertex‑form quadratic f = a(x−h)² + k in real time; observe how a changes the opening direction and width, h shifts the graph horizontally, k shifts it vertically, and the vertex stays at (h, k). The sliders enable interactive exploration of each parameter’s effect, showing vertical stretch or compression, reflection, and translation of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.