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Translation Along the x and y Axes

When you graph a quadratic equation, in many instances, you find that the vertex of the parabola you generate corresponds to the origin of the Cartesian plane (0, 0). The discussions of linear equations in Chapter 7 and elsewhere emphasize that while many linear equations cross or intersect with the origin of the Cartesian plane, by shifting an intercept value, you can raise or lower the intercept point. The same situation arises when you work with quadratic equations.

When you consider the coordinate pair that defines the vertex of a parabola, you deal with the minimum value of the parabola if it opens upward. You deal with the maximum value of the parabola if it opens downward. You can shift this value so ...

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