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Parabola Shifting Demonstration

Parabola Shifting Demonstration
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2016-03-14 22:43
FunctionCoordinate GeometrySlider AnimationGraphing
This example demonstrates the dynamic transformation of a parabola through parameterized shifting. It involves core mathematical concepts such as parabola equations, parametric equations, and dynamic geometric transformations. The construction utilizes GeoGebra commands/objects like points (c, d, e, f, g, h, k, p, q, r, s, t, u, u_1, u_3, v, v_1, v_2, t_1, c_1). It is suitable for high school mathematics students and teachers to understand function graph transformations and the impact of parameters on shapes.

GeoGebra Commands & Parameters

  1. y = x^(2)
  2. y = (2 * x^(2))
  3. y = (4 * x^(2))
  4. Conic f
  5. y = (1 / 2 * x^(2))
  6. y = (1 / 3 * x^(2))
  7. y = (1 / 10 * x^(2))
  8. y = x^(2) + 1
  9. y = x^(2) + 3
  10. y = x^(2) + 6
  11. y = x^(2) - 2
  12. y = x^(2) - 4
  13. y = (x + 1)^(2)
  14. y = (x + 3)^(2)
  15. y = x^(2) + (10 * x) + 25
  16. y = x^(2) - (4 * x) + 4
  17. y = x^(2) - (8 * x) + 16
  18. y = x^(2) - (16 * x) + 64
  19. y = x^(2) - 8
  20. y = (-x^(2))

AI Drawing Prompt Reference

Draw a standard parabola opening upwards y=x². Then, draw parabolas with different coefficients: y=(2x²), y=(4x²), y=(1/2x²), y=(1/3x²), y=(1/10x²). Next, shift the parabola up along the y-axis: y=x²+1, y=x²+3, y=x²+6, y=x²-2, y=x²-4. Shift the parabola left along the x-axis: y=(x+1)², y=(x+3)². Then, rewrite the equations by completing the square: y=(x+5)², y=(x-2)², y=(x-4)², y=(x-8)². Finally, draw a parabola opening downwards: y=-x².
The prompt above was compiled from the original drawing commands and is for reference only.