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Locus of the vertex as b varies

Locus of the vertex as b varies
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2014-07-19 20:40
FunctionLocus
This example demonstrates the path traced by the vertex of a parabola as the coefficient b varies. It involves core math concepts like parabolas, function graphs, and locus. Constructed using GeoGebra objects c, b, a, f, a_1, C, A. Suitable for high school mathematics education to understand the impact of parameter changes on function graphs.

GeoGebra Commands & Parameters

  1. Numeric c(1)
  2. Numeric b(-2.3)
  3. Numeric a(-1)
  4. f(x) = (a * x^(2)) + (b * x) + c
  5. Line a_1(12, 0, 0)
  6. Point C(-9.89, 7.6)
  7. (((-b)) / 2 / a, f(((-b)) / 2 / a))

AI Drawing Prompt Reference

Draw the locus of the vertex of a parabola as the coefficient b varies from -2.3 to 1, with a = -1 and c = 1. Include the x-axis, mark a point on the locus at the vertex of the parabola, and show the parabola changing as b varies to illustrate the impact of parameter changes on the function graph.
The prompt above was compiled from the original drawing commands and is for reference only.