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 $\"\"$ behave like $\"\"$ for large values of $\"\"$ .

Find the intercepts of the function :

$\"\"$

Find the $\"\"$ -intercepts by substituting $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ 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 $\"\"$ .

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 of 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 $\"\"$ :

$\"\"$ .

The function in factored form is $\"\"$

Step 1 : $\"\"$ .

Step 2 :

$\"\"$ - intercepts : $\"\"$ and $\"\"$ .

$\"\"$ - intercept : $\"\"$ .

Step 3 : Zeros are $\"\"$ and $\"\"$ : multiplicity $\"\"$ , crosses.

Step 4 : At most $\"\"$ turning points.

Step 5 :

Near $\"\"$ : $\"\"$ .

Step 6 : Graph of the function $\"\"$ :

$\"\"$