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Zeros of Quadratic Function with Graph

Zeros of Quadratic Function with Graph
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2016-08-19 01:44
FunctionComplex NumberGraphing
This example demonstrates the zeros of a quadratic function and its graphical representation. Key math concepts include quadratic functions, zeros, discriminant, complex numbers, and geometric transformations. It is constructed using GeoGebra commands like RandomElement, KeepIf, Intersect, Mirror, Circle, OrthogonalLine, and objects such as xmax, xmin, etc. Suitable for high school mathematics teaching to understand the properties of quadratic functions and graphical transformations.

GeoGebra Commands & Parameters

  1. 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
  2. KeepIf(x ≠ 0, Sequence[i, i, -3, 3 + If[rs, 0, 0]]) → list4a
  3. RandomElement(KeepIf[x ≠ 0, Sequence[i, i, -5, 5 + If[rs, 0, 0]]]) → numverSelectionwithExcluding
  4. KeepIf(x ≠ 0, Sequence[i, i, -3, 3 + If[rs, 0, 0]]) → list4b
  5. RandomElement(list4a) → rana
  6. RandomElement(list4b) → ranb
  7. Tool2(rana, ranc, ((2 * rana) * ranb)) → text1
  8. Intersect(f, xAxis) → A, B
  9. Mirror(f, g) → f_1
  10. Intersect(xAxis, f_1) → C, D
  11. Circle(M, C) → c
  12. OrthogonalLine(M, xAxis) → h
  13. Intersect(c, h) → E, F