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

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Inverting and Shifting Parabolas

In addition to inverting parabolas, you can shift them along the x axis. To shift a parabola, you set up an equation that involves using the square of the difference of two values. The equation with which you shift a parabola assumes the following form:

y = (xb)2

In this form of the equation, the value of b designates the distance along the x axis you want to shift the vertex of the parabola. If b is a positive number, then you shift the parabola to the right on the x axis. If b is a negative number, then you shift the parabola to the left. Here is how you can rewrite the equation when b consists of a negative value.

y = (x – (–b))2

y = (x + b)2

This equation shifts the parabola to the left on the x axis. ...

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