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Phantom Graph (x^2+1)^2

Phantom Graph (x^2+1)^2
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2018-07-22 18:54
FunctionCoordinate GeometryGraphing
In collections Phantom Graphs
This example demonstrates the phantom graph of (x^2+1)^2. The core mathematical concepts involved are quadratic functions. Using GeoGebra commands such as Plane, ComplexRoot, and CurveCartesian, the graph is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Plane((0, c, 0), (1, c, 0), (0, c, 1)) → p
  2. ComplexRoot(f(x) - c) → z_1, z_2, z_3, z_4
  3. CurveCartesian(0, (t^(2) - 1)^(2), t, t, -25, 25) → a
  4. CurveCartesian(t, (-4 * t^(4)) - (4 * t^(2)), sqrt(t^(2) + 1), t, -25, 25) → b
  5. CurveCartesian(t, (-4 * t^(4)) - (4 * t^(2)), (-sqrt(t^(2) + 1)), t, -25, 25) → d