Cubic Graphs
Drawing a Cubic
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Sketch the curve: \(y=(2-x)(x+1)^2\)
- This curve has a negetive x value, therefore it will look like a y=-x line with a wobble.
- The roots will be 2 and -1 and the y-intercept will be 2.
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Sketch the curve \(y=(x-4)^3\)
- The curve has roots 4, 4, and 4 causing a point of inflection at 4
- The curve as a y-intercept of -64.
A cubic with limited roots
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Sketch the curve with equation: \(y=(x-1)(x^2+x+1)\)
- -1 is the only root
- The y-intercept is 1
- We do not know where the wobble will be....