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The general form of a quadratic is "y = ax2 + bx + c". For graphing, the leading coefficient "a" indicates how "fat" or how "skinny" the parabola will be.

For | a | > 1 (such as a = 3 or a = –4), the parabola will be "skinny", because it grows more quickly (three times as fast or four times as fast, respectively, in the case of our sample values of a).

For | a | < 1 (such as a = 1/3 or a = –1/4 ), the parabola will be "fat", because it grows more slowly (one-third as fast or one-fourth as fast, respectively, in the examples). Also, if a is negative, then the parabola is upside-down.




You can see these trends when you look at how the curve y = ax2 moves as "a" changes.

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