The function is .

Determine the end behavior of the graph of the function :

Expand the polynomial.

.

The polynomial function of degree .

The graph of 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 touches the -axis at  .

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

Degree of the function is .

Therefore, the number of turning points .

At most turning points.

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

Near :

.

A parabola opening down.

Near :

.

A line with slope .

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

Plot the intercepts.

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

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

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

Graph of the function :

.

Step 1 : .

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

Step 3 :  : multiplicity , crosses ; : multiplicity , touches.

Step 4 : At most turning points.

Step 5 :

Near : .

Near : .

Step 6 : Graph of the function :

.