Demonstration of Cubic Equation Roots
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This example demonstrates the roots of cubic equations and their graphical representations. It involves core mathematical concepts such as cubic functions, properties of roots, and the effect of parameters on function graphs. Construction highlights the use of GeoGebra commands/objects: p (parameter), q (parameter), f (function), d (point), A (point), k (parameter), B (point). Suitable for high school mathematics education to understand the relationship between cubic equation roots and their graphs.
GeoGebra Commands & Parameters
Numeric p(-2.9)Numeric q(0.6)f(x) = x^(3) + (p * x) + q(-((4 * p^(3)) + (27 * q^(2))))((((-q)) / 2 + sqrt(q^(2) / 4 + p^(3) / 27))^(1 / 3) + (((-q)) / 2 - sqrt(q^(2) / 4 + p^(3) / 27))^(1 / 3), 0){0, 1, 2}(((2 * sqrt(((-p)) / 3)) * cos((1 / 3 * acos((((3 * q)) / ((2 * p)) * sqrt(((-3)) / p)))) - ((2 * (π * k))) / 3)), 0)