SOLUTION: I'm having trouble finding the answer Determine the end behavior of f(x) = 2x^2 (1+3x-x^2)

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Question 1085281: I'm having trouble finding the answer
Determine the end behavior of f(x) = 2x^2 (1+3x-x^2)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+2x%5E2+%281%2B3x-x%5E2%29
f%28x%29+=+-2x%5E4%2B6x%5E3%2B2x%5E2


Since leading term of the polynomial (the term in a polynomial which contains the highest power of the variable) is -2x%5E4, then degree is 4, i.e. even, and leading coefficient is -2, i.e. negative.
This means that f%28x%29-%3E-infinity as x-%3E-infinityand f%28x%29-%3E+-infinityas x-%3E+infinity.

+graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+-2x%5E4%2B6x%5E3%2B2x%5E2%29+