Describing Key Features of a Graph of a Polynomial Function:

Explain how to sketch a graph of the function f (x) = x3 + 2x2 - 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.

The degree of the function is odd and the leading coefficient is positive - so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity.

The zeroes are - 4, 0, and 2, all with multiplicity 1.

The function is negative from negative infinity to - 4 and from 0 to 2.

The function is positive from - 4 to 0 and from 2 to infinity.