Characteristics of Polynomial
Functions
Remember projectile motion…
A quadratic is really a combination of different power functions
The path of marine animals…
h(t) = t4 + t3 +…
What are the key features of
graphs of polynomial functions?...
TRACK:
1. End behaviour (D and R)
2. Number of minimum and maximum
points.
3. Local minimum and maximum points
4. Number of x intercepts
See sheet…
We have been given a polynomial
in graphical and algebraic form,…
there is one more form we may
see…
A table of values….
A core part of all scientific research
involves data collection….
The only way to write a general model
of a relationship is to start by looking
at a collection of specific cases
By looking at a graph, we can now attach a
model.
Is there a way to do it without graphing?....
• A difference table can be used to
analyze whether a given set of data points
fits into a particular polynomial model.
Consider your summer job…
Suppose you make $10/h
Hours
0
1
2
3
4
Pay
0
10
20
30
40
P
-----10 – 0 = 10
20 – 10 = 10
30 – 20 = 10
40 – 30 = 10
Slope!
Shows the
rate of
change
(which is a
constant!!)
Once we find that constant rate of change, then we know
how the function progresses from point to point…..
Consider y = x2 + 1
X
Y
-3
10
5
2
1
2
5
10
-2
-1
0
1
2
3
Y
Y2
------- --------
-5
-3
-1
1
3
5
--------
2
2
2
2
2
The second
difference is
constant, so
it must be a
polynomial of
degree 2!
Try y = x3 + 1
Note:
• The sign of the constant difference term is
also the sign of the leading coefficient.
• The leading coefficient “a” can be
determined using the following formula.
• CDterm = a[(n)(n-1)(n-2)(3)(2)(1), where n is
the degree of the polynomial.
What type of
polynomial?
Homework
• Pg 13 1 – 10
Harcourt Math 12: Ad Func and Intro Calc
(yellow text)