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Quadratic Functions Demo

Quadratic Functions Demo
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2014-09-02 00:08
FunctionTrigonometryCalculusOptimizationGraphing
This example demonstrates the graph and properties of quadratic functions, involving core concepts like quadratic functions, upper and lower sums (Riemann sums), trigonometry, piecewise functions, linear functions, and calculus. It uses commands and objects such as Random, Point, Vector, Rotate, Sequence, Element, and Textfield in GeoGebra for construction. Suitable for high school students learning function graphs, introductory calculus, and geometric transformations.

GeoGebra Commands & Parameters

  1. Random(1, 3) → D1
  2. Random(1, 3) → D2
  3. Random(1, 3) → D3
  4. Random(1, 3) → D4
  5. Random(1, 3) → D5
  6. Random(1, 3) → D6
  7. Random(0, 6) → C1
  8. Random(0, 6) → C2
  9. Random(0, 6) → C3
  10. Random(0, 6) → C4
  11. Random(0, 6) → C5
  12. Random(0, 6) → C6
  13. Point(xAxis) → A
  14. Point(yAxis) → B
  15. Vector(A) → u
  16. Vector(B) → v
  17. Rotate(u, Element[theta, 1]) → u'
  18. Rotate(v, Element[theta, 1]) → v'
  19. Sequence(Vector[Rotate[u, Element[theta, n]]], n, 1, 6) → vectors1
  20. Sequence(Vector[Rotate[v, Element[theta, n]]], n, 1, 6) → vectors2
  21. Sequence({{x(Element[vectors1, n])}, {y(Element[vectors1, n])}}, n, 1, 6) → em1
  22. Sequence({{x(Element[vectors2, n])}, {y(Element[vectors2, n])}}, n, 1, 6) → em2
  23. Sequence(Element[eig1, n] * Element[aspectratio, n] * Element[em1, n] * Transpose[Element[em1, n]], n, 1, 6) → comp1
  24. Sequence(Element[eig2, n] * Element[em2, n] * Transpose[Element[em2, n]], n, 1, 6) → comp2
  25. Sequence(Element[comp1, n] + Element[comp2, n], n, 1, 6) → hessians
  26. Element(hessians, 1) → matrix1
  27. Element(hessians, 2) → matrix2
  28. Element(hessians, 3) → matrix3
  29. Element(hessians, 4) → matrix4
  30. Element(hessians, 5) → matrix5
  31. Element(hessians, 6) → matrix6
  32. Textfield() → inputBox1
  33. Random(1, 5) → C8
  34. Random(1, 5) → C9
  35. Random(1, 5) → C10
  36. Random(1, 5) → C11

AI Drawing Prompt Reference

Create a graph demonstrating the properties of quadratic functions, involving randomly generated points and vectors, constructing multiple vectors through rotation and sequences, and calculating their combinations to form several matrices, while also displaying the images of linear and trigonometric functions, suitable for high school students learning function graphs, introductory calculus, and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.