The function is .

Determine the end behavior of the graph of the function :

Factor the polynomial function.

.

The polynomial function is of degree . The graph of f behave like for large values of .

Find the intercepts of the function:

Find the -intercepts by substituting in .

and .

and .

-intercepts are and .

Find the -intercepts by substituting in .

-intercept is .

Determine the zeros of the function and their multiplicity :

Use this information to determine whether the graph crosses or touches the -axis at each -intercept.

The zeros of the function are and .

The zero is a zero of multiplicity , so the graph of crosses the -axis at  .

The zero is a zero of multiplicity , so the graph of crosses the -axis at  .

The zero is a zero of multiplicity , so the graph of crosses the -axis at  .

Determine the maximum number of turning points on the graph of the function:

Degree of the function is .

Therefore, number of turning points

At most turning points .

Determine the behavior of the graph of near each -intercept:

Near :

A line with slope .

Near :

A line with slope .

Near :

A line with slope .

 Put all the information from the steps 1 through 5 together to obtain graph of .

Graph the intercepts.

Construct a table values to graph the general shape of the curve.

	\            \	\ \
	\ \	\ \
	\ \	\ \
	\ \	\ \
	\ \	\ \

 Plot the points found in the table and connect the plotted points.

Graph of the function :

.

Step 1: .

Step 2: -intercept is and -intercepts are and .

Step 3: Zeros are and ; multiplicity , crosses

Step 4: At most turning points.

Step 5: Near : .

Near : .

Near : .

Step 6: Graph of the function :

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