SOLUTION: I have a question that states: use the even and odd powers of (x-c) Theorem to determine where the graph of the given polynomial will cross the x-axis and where the graph will int

Question 86305: I have a question that states: use the even and odd powers of (x-c) Theorem to determine where the graph of the given polynomial will cross the x-axis and where the graph will intersect but not cross the x-axis. y=x(x-4)^2
Answer by scianci(186) (Show Source): You can put this solution on YOUR website!
y= x(x-4)^2 has 2 zeros ; one at 0 and one at 4. The factor generating the one at 0 is x, which is raised to an odd power [1 by default since there's none specified]. So the graph will cross the x-axis at x = 0 [the origin]
The factor generating the one at 4 is x - 4, which is raised to an even power, 2. So the graph will touch but not cross the x-axis at x = 4.
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