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Transforming and Sketching Parabolas

Transforming and Sketching Parabolas
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2020-06-21 19:00
FunctionCoordinate GeometryInequalityGraphing
This example demonstrates the transformation and sketching of parabolas, involving core math concepts like functions, coordinate geometry, inequalities, and analytical geometry. It utilizes GeoGebra commands and objects such as If, Intersect, LaTeX, Textfield, Point, OrthogonalLine, Segment, and TableText for construction. Suitable for high school students and educators for teaching and exploration purposes.

GeoGebra Commands & Parameters

  1. If(a ≟ 0, k, If[a ≟ 1 ∧ h ≟ 0, x^(2) + k, If[a ≠ 1 ∧ h ≟ 0, (a * x^(2)) + k, If[a ≟ 1 ∧ h ≠ 0, f(x + h) + k, (a * f(x + h)) + k]]]) → p
  2. Intersect(p, xAxis) → A, B
  3. Intersect(p, yAxis) → C
  4. LaTeX(p, true, true) → text8
  5. Textfield(h) → InputBox1
  6. Textfield(k) → InputBox2
  7. Textfield(a) → InputBox3
  8. Point(xAxis) → D
  9. OrthogonalLine(D, xAxis) → t
  10. Intersect(p, t) → F
  11. Intersect(f, t) → G
  12. Segment(D, G) → f_1
  13. Segment(G, F) → g_1
  14. OrthogonalLine(G, yAxis) → h_1
  15. OrthogonalLine(F, yAxis) → i_1
  16. Intersect(h_1, yAxis) → H
  17. Intersect(i_1, yAxis) → I
  18. Segment(G, H) → j_1
  19. Segment(F, I) → k_1
  20. Point(eq1) → J
  21. Point(eq1) → K
  22. Segment(K, J) → l_1
  23. TableText({{A1, B1, C1, D1, E1, F1, G1, H1}, {A2, B2, C2, D2, E2, F2, G2, H2}, {A3, B3, C3, D3, E3, F3, G3, H3}}, "c_|h") → text2