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Phantom Graph of (x^2+1)^2

Phantom Graph of (x^2+1)^2
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2018-07-15 10:52
FunctionCalculusComplex NumberGraphing
In collections Phantom Graphs
This example demonstrates the graph of the function (x^2+1)^2, highlighting its characteristics and behavior. Key math concepts include polynomial functions, graphing techniques, and complex number roots. It utilizes GeoGebra commands like ComplexRoot for calculating complex roots and CurveCartesian for plotting Cartesian curves. Suitable for high school and above, aiding in understanding the plotting and properties of complex functions.

GeoGebra Commands & Parameters

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