2. The graph of a polynomial function has the following
characteristics
 SMOOTH CURVE - the turning points are not sharp
 CONTINUOUS CURVE – if you traced the graph with a
pen, you would never have to lift the pen
 The DOMAIN is the set of real numbers
 The X – INTERCEPT is the abscissa of the point where
the graph touches the x – axis.
 ABSOLUTE MAXIMUM/MINIMUM is the highest or
lowest point (respectively) of the graph of a polynomial
function.
 RELATIVE MAXIMUM/MINIMUM are the turning points
of the graph of a polynomial function.

5. Value of Number of
P(x) Degree leading Rational Number of turning
(Odd/Even coefficient zeros x- points
) intercepts
1 Odd a >0 0 1 0
2 Odd a >0 2, 4, 6 3 2
3 Odd a< 0 4 1 2
4 Even a >0 0 1 1
5 Even a >0 1, -1, 2, -2 4 3
6 Even a< 0 none 0 1

6.  How would you relate number of turning
points with the degree of each function?
 What can be said about the number of zeros
that each graph has and its relationship
with the degree of its respective function?
 What seems to be true with the graph’s
behavior and its degree? the value of its
leading coefficient?

7.  A polynomial function of degree n has
 a maximum number of n-1 turning
points
 at most n x-intercepts

8. Leading Degree
coefficient (Odd/Even) Description of the Graph
a >0 Even Comes down from the left,
goes up to the right
a >0 Odd Comes up from the left,
goes up to the right
a< 0 Even Comes up from the left,
goes down to the right
a< 0 Odd Comes down from the left,
goes down to the right

9. f ( x) x3

15.  Describe the behavior of the following
polynomial functions and identify the number
of maximum zeros and turning points.
4 2
1. f ( x) x 13x 36
4 3 2
2. f ( x) 2x 2x 8x 8x
4 2
3. f ( x) x 13x 36