Question

Use the key features of the polynomial f(x) = −4x4 + 4x3 + 9x2 − 12x + 10 to describe its end behavior.

Answer 1

Answer:

The end behavior of a polynomial is determined by its grade, if it's an odd polynomial or an even polynomial. Also, another important characterstic is the leading coeffcient, because if it's positive, then the function will open to positive territory, this apply the most to even polynomials.

The given expression is

$f(x)=-4x^{4} +4x^{3}+9x^{2} -12x+10$

As you can notice, the polynomial function has a grade of 4, that means it's an even function, with negative leading coefficient.

Therefore, the given function open towards negative side, that means it's end behavior is downside.

The image attached shows the graph of the function, there you can observe the end behavior we determined.