If you consider the examples quadratic equations offered in the previous sections, you find that the standard form of the equation can prove useful as a way to easily discern the basic features of the parabola the equation generates. To recapitulate, consider again the extended form of the equation:

a (x – h)^{2} + k

If you know the value of a, then you can determine how wide or narrow the parabola is likely to appear. If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. If the value of h is positive, then the vertex of the parabola shifts to the right, or positive, direction on the x axis. If it is negative, then the vertex of the parabola shifts to the left, or negative, direction on the

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