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Quadratic Function Machine: Interactive Visualization of Quadratic Functions wit

Quadratic Function Machine: Interactive Visualization of Quadratic Functions wit
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2020-11-13 01:03
TriangleFunctionTrigonometryTransformationGraphing
① This interactive 'machine' dynamically demonstrates the graph of a quadratic function and its connections with trigonometric functions, similar triangles, and other geometric elements, allowing users to adjust parameters and observe changes. ② Core mathematical concepts include quadratic functions (parabolas), roots (zeros), trigonometry, similar triangles, dilation (scaling), and intersections. ③ Construction highlights: The example uses GeoGebra commands such as CurveCartesian, Circle, Polygon, Point, Textfield, Vector, Semicircle, Mod, Segment, LaTeX, TextToUnicode, Text, Remove, RemoveUndefined, and Element to build a complex interactive scene with multiple points, polygons, segments, and dynamic text. ④ Suitable for high school or pre-university students learning quadratic functions, trigonometry, and geometric transformations, as well as for teachers to demonstrate the deep connections between functions and geometry in class.

GeoGebra Commands & Parameters

  1. CurveCartesian(x(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * cos(t + v)), y(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * sin(t + v)), t, 0, 6.28319) → c
  2. CurveCartesian(x(B) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * cos(t - v)), y(B) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * sin(t - v)), t, 0, 6.28319) → d
  3. Circle(B, R + 0.9) → e
  4. Circle(A, r + 0.9) → g
  5. Circle(A, r + 0.9) → h
  6. CurveCartesian(x(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * cos(t + v)), y(A) + ((r * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * sin(t + v)), t, 0, 6.28319) → i
  7. CurveCartesian(x(C) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * cos(t - v)), y(C) + ((R * (a + (1 / b * tanh((b * sin((n * t) - v)))))) * sin(t - v)), t, 0, 6.28319) → j
  8. CurveCartesian(x(C) + ((r / 2 * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * cos(t + v)), y(C) + ((r / 2 * (a + (1 / b * tanh((b * sin((n * t) + v)))))) * sin(t + v)), t, 0, 6.28319) → o
  9. Polygon(D, E, F, G) → poly1, d_1, e_1, f_1, g_1
  10. Point(g_1) → H
  11. Point(g_1) → I
  12. Polygon(H, I, J, K) → poly2, h_1, i_1, j_1, k
  13. Polygon(L, K, J, M) → poly3, l, k_1, j_2, m
  14. Point(f_1) → N
  15. Polygon(N, O, P, F) → poly4, n_1, o_1, p, f_2
  16. Textfield(s) → ChampTexte1
  17. Vector(Q, S) → u
  18. Textfield(f) → ChampTexte2
  19. Vector(U, V) → w
  20. Vector(W, Z) → z
  21. Polygon(C_1, M, L, D_1) → poly5, c_1, m_1, l_1, d_2
  22. Polygon(E_1, F_1, G_1, H_1) → poly6, e_2, f_3, g_2, h_2
  23. Semicircle(F_1, G_1) → q
  24. Mod(v / °, 2) → t_1
  25. Semicircle(F_1, G_1) → p_1
  26. Segment(A_1, B_1) → a_1
  27. LaTeX(f) → textFromFunction
  28. TextToUnicode(textFromFunction) → L_3
  29. Text("(" + s + ")") → textFormulaValue
  30. TextToUnicode(textFormulaValue) → L_n
  31. Remove(Insert[L_n, L_3, IndexOf[120, L_3]], {120}) → L_4
  32. Remove(Insert[L_n, L_4, IndexOf[120, L_4]], {120}) → L_5
  33. Remove(Insert[L_n, L_5, IndexOf[120, L_5]], {120}) → L_6
  34. Remove(Insert[L_n, L_6, IndexOf[120, L_6]], {120}) → L_7
  35. Remove(Insert[L_n, L_7, IndexOf[120, L_7]], {120}) → L_8
  36. Remove(Insert[L_n, L_8, IndexOf[120, L_8]], {120}) → L_9
  37. RemoveUndefined({L_3, L_4, L_5, L_6, L_7, L_8, L_9}) → L_{10}
  38. Element(L_{10}, Length[L_{10}]) → L_{11}
  39. LaTeX("= " + (UnicodeToText[L_{11}]), true) → textEnumFunction

AI Drawing Prompt Reference

Draw a dynamic quadratic function graph with adjustable parameters, including related trigonometric function graphs. First, draw two dynamic curves, then add two circles, followed by multiple dynamic curves and polygons, and finally add text and vectors to show the relationship between the quadratic function and trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.