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Comparing Standard and Vertex Forms of Parabolas

Comparing Standard and Vertex Forms of Parabolas
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2013-08-03 23:25
FunctionCoordinate GeometryGraphing
In collections Geom Graph Parabolas
This example demonstrates the comparison of graphs between standard form (ax^2+bx+c) and vertex form (a(x-h)^2+k) of parabolas. It involves core math concepts like quadratic functions, parabolas, and the transformation between these forms. The construction uses GeoGebra objects: a, b, c, h, k, f, g. It is suitable for high school students to understand the properties and conversion of parabolas in different forms, as well as for teaching purposes.

GeoGebra Commands & Parameters

  1. Numeric a(1.0)
  2. Numeric b(0.0)
  3. Numeric c(-1.0)
  4. Numeric h(2.6)
  5. Numeric k(-1.0)
  6. f(x) = a * (x - h)^(2) + k
  7. g(x) = a * x^(2) + b * x + c

AI Drawing Prompt Reference

Plot two parabolas, one using vertex form a(x-h)^2+k with a=1, h=2.6, k=-1, and the other using standard form ax^2+bx+c with b=0, c=-1, to demonstrate their relationship and transformation.
The prompt above was compiled from the original drawing commands and is for reference only.