Symmetry of 1/x^2 Function
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This example demonstrates the symmetry of the function y=1/x^2, involving core math concepts like inverse proportionality function, symmetry, parametric curves, curve sketching, median line, fractal geometry, and standard deviation. It utilizes GeoGebra commands/objects such as f (function), t (parameter), A, B (points), i (iteration), g (graphics), and K (constant). Suitable for high school and above learners to understand the properties of inverse proportionality function graphs and the application of parametric equations.
GeoGebra Commands & Parameters
f(x) = 1 / x^(2)Numeric t(2.2)(t, f(t))(1 / sqrt(t), t)y - 1 / t^(2) = (t^(3) / 2 * (x - t))y - t = (1 / (((2 * t) * sqrt(t))) * (x - 1 / sqrt(t)))((((t^(3) + 3) * (t^(3) - 1))) / (t^(5) - sqrt(t)), (((2 * t^(7)) * sqrt(t)) - 2 + t^(6) - (t^(4) * sqrt(t))) / (((2 * t^(6)) * sqrt(t)) - (2 * t^(2))))