The polynomial function is .

(a)

 1.Find zeros of the polynomial.

Real zeros are the x - intercepts of the graph.

2. Test points.

Choose values for x and find the corresponding values for y. 

\ x \		(x, y )
\ \

3. End behavior.

.

Degree of polynomial is 4 and leading coefficient 1.

The graph of a polynomial function is always a smooth curve; that means, it has no breaks or corners.

All even degree polynomials behave on their ends like quadratics.

All even degree polynomials are either up on both ends and or down on both ends.depending on whether the polynomial has, respectively, a positive or negative leading coefficient.

The above polynomial even degree  polynomial with a positive leading coefficient .

So the graph up on both ends.

4. Graph:

1.Draw a coordinate plane.

2.Plot the intercepts and coordinate points found in the table.

3.Then sketch the graph, connecting the points with a smooth curve.

(b)

The function is .

To find the zeros of the function, equate f(x) to 0.

The real zeros of the function are .

(c)

The function is .

The real zeros of the function are , and

The x- intercepts are .

The real zeros of the function are the x - intercepts of the graph of the function.

(a) The graph of is :

(b) The real zeros of the function are .

(c) The real zeros of the function are the x - intercepts of the graph of the function.