(a)

The degree polynomial function has a leading coefficient .

The polynomial function .

Since the degree of polynomial is even (n = 4) and leading coefficient is positive (),  the graph rises to the left and right.

(b)

Find the real zeros of the function, by equating to zero.

Thus, the real zeros are and .

Since the x - intercepts occur at .

The real zeros are and .

(c)

The polynomial function is .

Choose different values of and find corresponding values for .

Make the table

(d)

The factor , k > 1, yields a repeated zero x = a of multiplicity k.

If k is odd, then the graph crosses the x - axis at x = a.

If k is even, then the graph touches the x - axis ( but does not cross the x - axis ) at x = a.

The polynomial function is .

The factor form of polynomial function .

The real zeros are and .

The exponent is greater than 1, the factor yields the repeated zero x = 0.

The zero of " g " , i.e, x = 0 has an even multiplicity because k = 2.

So, the graph touches the x - axis ( but does not cross the x - axis ) at x = 0.

The remaining zeros of " g " are and have an odd multiplicity because k = 1.

So, the graph crosses the x - axis at and .

1. Draw a coordinate plane.

2. Plot the x  - intercepts.

3. Plot the points obtained from the table.

3. Then draw a curve connecting those points.

Graph :

(a)

The graph rises to the left and right.

(b)

The real zeros are and .

(c)

The table is : \ \

(d)

The graph of the function is : \ \