SOLUTION: What is the end behavior of f(x)=2x(x-4)^2?

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Question 956933: What is the end behavior of f(x)=2x(x-4)^2?
Found 2 solutions by Fombitz, addingup:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
As x goes to infinity, the function goes to infinity like x%5E3.
As x goes to -infinity, the function goes to -infinity like x%5E3.
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graph%28300%2C300%2C-10%2C10%2C-100%2C100%2C2x%2A%28x-4%29%5E2%29

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2x%28x-4%29%5E2 Look at the squared operation, %28x-4%29%5E2. This is the same as (x-4)(x-4), since the square of a number equals the number times itself. Now we have:
2x%28x-4%29%28x-4%29 Let's follow F.O.I.L. to get rid of the parenthesis:
x%2Ax-4x-4x%2B16+=+x%5E2-8x%2B16 So we now have:
2x%28x%5E2%2B8x%2B16%29. Here we have: 2x%2Ax%5E2=+2x%5E3 and 2x%2A8x=+16x%5E2 and 2x%2A16=+32x:
2x%5E3-16x%5E2%2B32xThis is your answer.