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Phantom Graph of y=x^2/((x-1)(x-4))

Phantom Graph of y=x^2/((x-1)(x-4))
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2018-07-15 11:03
FunctionCoordinate GeometryComplex Number
In collections Phantom Graphs
This example demonstrates the phantom graph of the function y=x^2/((x-1)(x-4)). It involves complex numbers and coordinate geometry. Using GeoGebra commands such as ComplexRoot, Plane, and CurveCartesian, the graph of the function can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. ComplexRoot(x^(2) - (c * (x^(2) - (5 * x) + 4))) → z_1, z_2
  2. Plane((0, c, 0), (1, c, 1), (-1, c, 2)) → e
  3. CurveCartesian((5 * t / ((2 * t) - 2)), t, sqrt(((-9 * t^(2)) - (16 * t)) / ((4 * (t - 1)^(2)))), t, -16 / 9, 0) → a
  4. CurveCartesian((5 * t / ((2 * t) - 2)), t, (-sqrt(((-9 * t^(2)) - (16 * t)) / ((4 * (t - 1)^(2))))), t, -16 / 9, 0) → b
  5. CurveCartesian(t, (2 * t / ((2 * t) - 5)), sqrt((8 * t / 5) - t^(2)), t, 0, 8 / 5) → h
  6. CurveCartesian(t, (2 * t / ((2 * t) - 5)), (-sqrt((8 * t / 5) - t^(2))), t, 0, 8 / 5) → i