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Vertical Parabola Shifts Demo

Vertical Parabola Shifts Demo
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2017-04-22 18:37
FunctionCoordinate GeometryGeometric ConstructionLocus
In collections Conics Investigation
This example demonstrates the geometric transformation of vertical shifts in parabolas. It involves core math concepts like parabola definition, focus-directrix relationship, linear function graphs, and analytical geometry point-line interactions. Construction highlights include commands/objects like Point, Segment, OrthogonalLine, Intersect, Distance, Angle, Midpoint from GeoGebra. Suitable for high school analytical geometry instruction to understand standard parabola equations and their translation transformations.

GeoGebra Commands & Parameters

  1. Parabola(Focus, Directrix) → c
  2. Point(c) → P
  3. Segment(Focus, P) → g
  4. OrthogonalLine(P, Directrix) → h
  5. Intersect(Directrix, h) → C
  6. Segment(C, P) → i
  7. Distance(Focus, P) → distanceAB
  8. Distance(C, P) → distanceCB
  9. Angle(Directrix, i) → α
  10. OrthogonalLine(Focus, Directrix) → f
  11. Intersect(Directrix, f) → A
  12. Segment(Focus, A) → j
  13. Midpoint(Focus, A) → B