MathPlotAI Logo MathPlotAI

Parabola through 3 random points: Vertex in square?

Parabola through 3 random points: Vertex in square?
Loading the math board and drawing, please wait…
2020-01-26 20:03
Coordinate GeometryProbability & StatisticsOptimization
This example demonstrates fitting a parabola through three randomly generated points and investigates whether its vertex lies within a specified square. Key math concepts include parabolas, stochastic processes, standard deviation, geometric constructions, and derivatives. GeoGebra commands like Polygon, RandomPointIn, FitPoly, Extremum, IsInRegion, Sum, and Length are used to construct the visualization. Suitable for high school and above, exploring the interplay of randomness, geometry, and function graphs.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (1, 0), 4) → poly1
  2. RandomPointIn(poly1) → A
  3. RandomPointIn(poly1) → B
  4. RandomPointIn(poly1) → C
  5. FitPoly({A, B, C}, 2) → f
  6. Extremum(f) → V
  7. IsInRegion(V, poly1) → a
  8. Sum(data) → b
  9. Length(data) → c

AI Drawing Prompt Reference

Generate three random points inside a square, fit a parabola through these points, find the vertex of the parabola, and check if it lies within the square. Display the square, random points, parabola, and the vertex's position relation.
The prompt above was compiled from the original drawing commands and is for reference only.