Quadratic Graphs

The general form of a quadratic is "*y* = *ax*^{2} + *bx* + *c*". For graphing, the leading coefficient "*a*" indicates how "fat" or "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.

Straight line graphs

horizontal and vertical lines: "x=a" and "y=a"

x=a is a vertical line through "a" on the x-axis

y=a isa horizontal line through "a" on the y-axis

Remember:

the y-axis is also the line x=0, the x-axis is also the line y=0

the main diagonals: "y=x" and "y=-x"

y=x is the main diagonal that goes UPHILL from left to right.

y=-x is the main diagonal that goes DOWNHILL from left to right.

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