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Graphs of y^2 = kx

Graphs of y^2 = kx
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2014-01-01 11:40
FunctionCoordinate Geometry
This example demonstrates the graphs of the parabola y^2 = kx as the parameter k varies, covering core concepts in coordinate geometry and parametric equations. It utilizes GeoGebra commands like K_1, c, k_2, d, a, a_1, etc., to construct and animate the parabola, making it suitable for high school and advanced learners studying parabolic properties and parameter effects.

GeoGebra Commands & Parameters

  1. Numeric K_1(1.0)
  2. y^(2) = (K_1 * x)
  3. Numeric k_2(-1.0)
  4. y^(2) = (k_2 * x)
  5. Boolean a(false)
  6. Numeric a_1(2.0)
  7. Numeric a_2(-2.0)
  8. Numeric b_1(3.0)
  9. Numeric b_2(-3.0)
  10. Numeric c_1(4.0)
  11. Numeric c_2(-4.0)
  12. Numeric d_1(5.0)
  13. Numeric d_2(-5.0)
  14. y^(2) = (a_2 * x)
  15. y^(2) = (a_1 * x)
  16. Boolean b(false)
  17. y^(2) = (b_1 * x)
  18. y^(2) = (b_2 * x)
  19. Boolean i(false)
  20. y^(2) = (c_1 * x)
  21. y^(2) = (c_2 * x)
  22. Boolean j(false)
  23. y^(2) = (d_1 * x)
  24. y^(2) = (d_2 * x)
  25. Boolean l(false)

AI Drawing Prompt Reference

Draw parabolas of the form y^2 = kx where k can be 1, -1, 2, -2, 3, -3, 4, -4, 5, and -5. Start by drawing the parabolas for k=1 and k=-1, then draw the parabolas for k=2 and k=-2, k=3 and k=-3, k=4 and k=-4, and k=5 and k=-5.
The prompt above was compiled from the original drawing commands and is for reference only.