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Sketch the graph of a polynomial:
Solution:
Consider the given equation above
Since the given equation, is already factored, then we can get the x-intercepts by setting y = 0. The x-intercepts are 1, -1, and 2.
If we set x = 0, the y-intercept of the given equation is
Since we now the x-intercepts, then we can sketch the location or direction of a curve as follows
If x < -1, then y = (-)(-)(-) = (-)
If -1 < x < 0, then y = (-)(+)(-) = (+)
If 0 < x < 1, then y = (-)(+)(-) = (+)
If 1 < x < 2, then y = (+)(+)(-) = (-)
If x > 2, then y = (+)(+)(+) = (+)
Here's the graph of a polynomial:
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| Photo by Math Principles in Everyday Life |