SOLUTION: What is the end behavior of the graph of the polynomial function f(x) = 3x^6 + 30x^5 + 75x^4?

Question 999619: What is the end behavior of the graph of the polynomial function f(x) = 3x^6 + 30x^5 + 75x^4?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
What is the end behavior of the graph of the polynomial function?
recall:
All even-degree polynomials behave, on their ends, like quadratics, and all odd-degree polynomials behave, on their ends, like cubics.
consider are the sign and the degree of the leading term;
in your case the exponent says that this is a degree 6 polynomial, so the graph will behave roughly like a quadratic: up on both ends or down on both ends
since the sign on the leading coefficient is positive, the graph will be on

=>even-degree polynomial with positive leading coefficient which means the graph will behave roughly like a quadratic an will be on

now we can find solutions to this function:

roots:

if => (multiplicity four)
if => (multiplicity two)

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