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Quadratic Functions and Minima

Quadratic Functions and Minima
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2018-08-29 13:11
FunctionCoordinate GeometryOptimization
This example demonstrates the graph of quadratic functions and the behavior of their minimum values. Key math concepts include quadratic functions, minimum values, and coordinate geometry. Constructed using GeoGebra commands like RandomElement, Point, Ellipse, and Textfield. Suitable for high school mathematics education and understanding function properties.

GeoGebra Commands & Parameters

  1. RandomElement({1, 2}) → r2
  2. RandomElement({1, 0.5, 1.5, 3, 6, 12, 15, -0.5, -5, -4, -2}) → r1
  3. RandomElement({0.5, 0.7, 0.6}) → ratio
  4. RandomElement({8, 10, 15}) → b
  5. Point({r1, r2}) → c
  6. RandomElement({π / 6, π / 4, ((-π)) / 3, ((-π)) / 4, ((-π)) / 6}) → theta
  7. Point({temp, temp2}) → end1
  8. Point({tem, tem2}) → end2
  9. Point({e1x, e1y}) → e11
  10. Point({e2x, e2y}) → e22
  11. Ellipse(e11, e22, end2) → d
  12. Textfield() → InputBox2
  13. RandomElement({10, 15, 20}) → InputBox1
  14. RandomElement({10, 20}) → InputBox3
  15. RandomElement({10, 15, 20}) → fval