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Graphing Polynomial Functions

Graphing Polynomial Functions
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2016-08-19 08:58
FunctionCalculusGraphing
This example demonstrates the graphing of polynomial functions. Key mathematical concepts include the properties and graph characteristics of polynomial functions. Using GeoGebra commands such as RandomElement, Random, Vector, and Textfield, users can dynamically adjust the coefficients of the polynomial function and observe changes in its graph. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. RandomElement(list4c) → c
  2. RandomElement(KeepIf[x > b1, list4b2]) → b2
  3. RandomElement(KeepIf[(x ≠ 0) ∧ (x ≥ Max[xmin, ymin]) ∧ (x ≤ Min[xmax, ymax]), Sequence[i, i, (-abs((xmin * ymin))), abs((xmax * ymax)) + If[rs, 0, 0]]]) → numbersectionexam
  4. RandomElement(KeepIf[x ≠ 0, Sequence[i, i, -5, 5 + If[rs, 0, 0]]]) → numverSelectionwithExcluding
  5. Random(1, 10 + If[rs, 0, 0]) → ranf
  6. Vector(A, B) → u
  7. Vector(C, D) → v
  8. Vector(A, F) → w
  9. Vector(C, E) → g
  10. Textfield(finput) → InputBox1
  11. Textfield(interinput1) → InputBox2
  12. Textfield(interinput2) → InputBox3
  13. Textfield(interinput3) → InputBox4
  14. If(ranf ≟ 2 ∨ ranf ≟ 9, 1, If[ranf ≟ 4 ∨ ranf ≟ 6, 3, If[ranf ≟ 5 ∨ ranf ≟ 7, 4, 2]]) → ninter
  15. If(ninter ≟ 2 ∧ (b1 < 0) ∨ ninter ≟ 3 ∧ (b1 < 0) ∨ ninter ≟ 1 ∨ ninter ≟ 4, b1, 0) → inter1x
  16. If(ninter ≟ 2 ∧ (b1 < 0) ∨ ninter ≟ 3 ∧ (b1 < 0) ∧ (0 < b2), 0, If[ninter ≟ 2 ∧ (0 < b1) ∨ ninter ≟ 3 ∧ (0 < b1), b1, b2]) → inter2x
  17. If(ninter ≟ 3 ∧ (b2 < 0), 0, b2) → inter3x
  18. Point(xAxis) → P1
  19. Point(Segment[P1 + (1, 0), (x(Corner[2]), 0)]) → P2
  20. Point(Segment[P2 + (1, 0), (x(Corner[2]), 0)]) → P3