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Parabolas and Reflection Construction

Parabolas and Reflection Construction
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2019-06-04 04:44
FunctionCoordinate GeometryTransformationGeometric Construction
This example demonstrates the geometric construction of parabolas and their reflection properties. Key math concepts include parabola, reflection, geometric mean, and symmetry. It uses GeoGebra commands like Vector, Translate, and Mirror to construct points, vectors, and figures. Suitable for high school coordinate geometry teaching or mathematical exploration.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Translate(f, u) → f_1
  3. Translate(f_1, u) → g
  4. Translate(g, u) → g_1
  5. Translate(g_1, u) → h
  6. Translate(h, u) → h_1
  7. Translate(h_1, u) → p
  8. Translate(p, u) → p_1
  9. Mirror(f_1, yAxis) → a
  10. Mirror(g, yAxis) → g_2
  11. Mirror(g_1, yAxis) → b
  12. Mirror(h, yAxis) → h_2
  13. Mirror(p, yAxis) → p_2
  14. Mirror(h_1, yAxis) → c
  15. Mirror(p_1, yAxis) → d

AI Drawing Prompt Reference

Construct a parabola and its reflection. First, create vector u from points A and B, then translate the parabola f to get f_1, and continue to translate to get g, g_1, h, h_1, p, and p_1. Reflect f_1 across the y-axis to get a, reflect g to get g_2, reflect g_1 to get b, reflect h to get h_2, reflect p to get p_2, and finally reflect h_1 to get c, and reflect p_1 to get d.
The prompt above was compiled from the original drawing commands and is for reference only.