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Exploration of Inverse of Quadratic Functions

Exploration of Inverse of Quadratic Functions
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2016-12-03 00:58
FunctionCoordinate GeometryGraphing
This example demonstrates the inverse of quadratic functions. By adjusting parameters, you can observe the changes in the quadratic function graph and its inverse. Key mathematical concepts include quadratic functions, inverse functions, and function graphs. GeoGebra commands used include functions, slider animation, and locus. Suitable for high school mathematics education and learning about quadratic functions and their inverses.

GeoGebra Commands & Parameters

  1. Numeric a(-3.503)
  2. f(x) = If[a ≤ x ≤ Infinity, (3 * (x - 2)^(2)) + 1]
  3. b: x = f(y)
  4. Numeric c(4.5)
  5. h(x) = (-((x - 1) / 3)^(1 / 2)) + 2
  6. g(x) = ((x - 1) / 3)^(1 / 2) + 2
  7. x = c
  8. y = x
  9. (c, g(c))
  10. (c, h(c))
  11. 0
  12. 1
  13. 2
  14. 3
  15. 4
  16. 5
  17. 6
  18. 7
  19. f(A2)
  20. f(A3)
  21. f(A4)
  22. f(A5)
  23. f(A6)
  24. f(A7)
  25. f(A8)
  26. f(A9)
  27. 1
  28. 2
  29. 3
  30. 4
  31. 5
  32. 6
  33. 7
  34. f(B13)
  35. f(B14)
  36. f(B15)
  37. f(B16)
  38. f(B17)
  39. f(B18)
  40. f(B19)
  41. 0
  42. f(B12)
  43. Boolean d(false)
  44. Boolean k(false)
  45. Boolean e(false)
  46. Boolean l(false)
  47. Boolean m(false)
  48. Numeric n(3.9)
  49. (n * f(n))
  50. (n, f(n))
  51. (f(n), g(f(n)))
  52. Boolean p(false)
  53. (2, 1)

AI Drawing Prompt Reference

Draw a quadratic function with vertex at (2,1) and display its inverse function. Adjust parameter a from -3.503 to infinity to observe changes in the quadratic function and its inverse. The quadratic function is y = 3(x - 2)² + 1, and the inverse functions are y = ±√(x - 1)/3 + 2.
The prompt above was compiled from the original drawing commands and is for reference only.