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Behavioral Mathematics for Game AI by Dave Mark

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Quadratic Functions

We can create another common and useful function in a similar fashion to the linear function above. By inserting an exponent into the formula, we create one of the veritably plethoric varieties of quadratic functions. Rather than being a straight line, the quadratic family exhibits parabolic curves. The most simple of these equations is the familiar

y = xk

This function creates a parabola centered on the y-axis whose vertex (the point where the parabola changes direction) crosses the origin. The exponent (k) can be any non-zero ...

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