The function f(x) = x 4 - 3 x 2 is the Mexican Hat function. It has the appearance of a Mexican Hat, hence its name. It is symmetric with respect to the y-axis ( x -> -x ). Its two minima produce two stable points when viewed as a potential function in Physics and Engineering.
The Skewed Mexican Hat function is the Mexican Hat function tilted by adding a linear term to the function. It has the form f(x) = x 4 - 3 x 2 - x. It has lost its symmetry with respect to the y-axis, and its two minima are now asymmetrical in location and value.
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