(a)

Find the least possible degree and end behavior.

Observe the graph of the polynomial function.

There are three turning points.

Since the graph has three turning points, the degree of the polynomial function is .

The end behavior of the graph is and .

(b)

Locate the zeros and their multiplicity. Assume all of the zeros are integral values.

Observe the graph of the polynomial function.

There are three zeros at , and .

Since the graph appears to be tangent to the -axis at , the zero has multiplicity .

(c)

Create a function that fits the graph and the given point.

If the zeros of the polynomial function are , and , then , and are the factors of the polynomial.

Thus, the polynomial function is , where is a constant.

Since the point lies on the graph, substitute in .

Substitute in .

Thus, the polynomial function is .

(a) The degree is and the end behavior of the graph is and .

(b) There are three zeros at , and , and the zero has multiplicity .

(c) The polynomial function is .