Unit 5 Enrichment: Finite Differences
We learned about first differences and can use first differences to
determine if a set of points create a linear or non-linear relation.
There are also second differences. These are the differences of the first
differences. There are also third differences, fourth differences and so on.
These differences are called finite differences. Finite differences can be
used to determine the degree of a relation.
Complete the following handout using a graphing calculator. Refer to the
handout from 5-5, if necessary.
1.
a) Graph y  x 2 . Sketch the graph on the given grid.
b) What is the degree of y  x 2 ? What do we call a polynomial of this
degree?
b) Use the calculator to fill in the y-coordinates of the points on the
graph.
c) Calculate finite differences until you find a finite difference that
is constant.
x
y
1st
diff
-3
-2
-1
0
1
2
3
1
2.
Explore other functions with different degrees and calculate finite
differences until you find a finite difference that is constant.
3.
State a rule using finite differences that can be used to determine
the degree of a polynomial function.
4.
Use your rule to determine the degree of the polynomial whose points
are given in the following table of values.
x
-3
-2
-1
0
1
2
3
y
-36
0
6
0
0
24
90
2