The function is $\"\"$ .

Determine the end behavior of the graph of the function:

Expand the polynomial.

$\"\"$

$\"\"$ .

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 $\"\"$ .

$\"\"$ -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 $\"\"$ touches 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 parabola that opens up.

Near $\"\"$ :

$\"\"$

A parabola that opens up.

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: $\"\"$ and $\"\"$ ; multiplicity $\"\"$ , touches

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

Step 5: Near $\"\"$ : $\"\"$ .

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

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

$\"\"$ .