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Parabola Investigation by David Cox

Parabola Investigation by David Cox
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2012-02-28 05:23
FunctionCoordinate GeometryTransformationGraphing
In collections Quadratic functions
This example demonstrates the effects of parameters a, b, and c on the graph of a parabola. It involves core mathematical concepts such as quadratic functions and the geometric transformation of function graphs due to parameter changes. The construction utilizes GeoGebra commands/objects like OrthogonalLine, Intersect, Segment, Distance, and Point. It is suitable for high school students to learn and understand the rules of function graph transformations and for mathematical exploration activities.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, yAxis) → d
  2. OrthogonalLine(B, yAxis) → e
  3. OrthogonalLine(C, yAxis) → g
  4. OrthogonalLine(D, yAxis) → h
  5. OrthogonalLine(G, xAxis) → i
  6. OrthogonalLine(F, xAxis) → j
  7. OrthogonalLine(E, xAxis) → k
  8. OrthogonalLine(B, xAxis) → l
  9. OrthogonalLine(C, xAxis) → m
  10. OrthogonalLine(D, xAxis) → n
  11. Intersect(g, i) → H
  12. Intersect(e, j) → I
  13. Intersect(d, k) → J
  14. Intersect(d, l) → K
  15. Intersect(e, m) → L
  16. Intersect(g, n) → M
  17. Segment(A, K) → p
  18. Segment(K, B) → q
  19. Segment(B, L) → r
  20. Segment(L, C) → s
  21. Segment(C, M) → t
  22. Segment(M, D) → a_1
  23. Segment(A, J) → b_1
  24. Segment(J, E) → c_1
  25. Segment(E, I) → d_1
  26. Segment(I, F) → e_1
  27. Segment(F, H) → f_1
  28. Segment(H, G) → g_1
  29. Distance(a_1, s) → o
  30. Distance(q, c_1) → u
  31. Distance(e_1, g_1) → v
  32. Point(j_1) → P
  33. Intersect(f, xAxis) → Q, R