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Beginning Pre-Calculus for Game Developers by Boris Meltreger, John P. Flynt

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Varieties of Translation

Translating the curves generated by equations with exponents entails performing operations similar to those you perform with linear equations. On one basic level, translation involves moving the vertex of a parabola along the y axis. To move a vertex along the y axis, you first consider the position of a parabola with its vertex resting on the origin of the Cartesian plane. You can then add values to this position to shift it up or down the y axis.

Parabolas

When you calculate values for a parabola, you use an exponent of an even value. The result is a graph that is symmetrical with respect to the y axis. A parabola crosses the y axis once, so if you employ an equation of the form y = x2 + c, the value of c provides ...

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