Cc-26 Polynomial Functions Examples And Worksheet - Common Core Page 5
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8Suppose you are given a set of polynomial function outputs. You know that their inputs
are an ordered set of x-values in which consecutive x-values differ by a constant. By
analyzing the differences of consecutive y-values, it is possible to determine the
least-degree polynomial function that could generate the data.
If the first differences are constant, the function is linear. If the second differences
(but not the first) are constant, the function is quadratic. If the third differences (but
not the second) are constant, the function is cubic, and so on.
Problem 4
Using Differences to Determine Degree
What is the degree of the polynomial function that generates
x
y
the data shown at the right?
3
1
2
7
A set of
Degree of the
Check first differences of y-values. Then
1
3
polynomial
polynomial function
check second differences, third differences,
function
and so on until they are constant.
0
5
values
1
11
2
9
y-value
1st
2nd
3rd
3
7
difference
difference
difference
1
6
10
7
6
4
4
3
How do you find the
second differences?
8
6
Subtract the consecutive
2
5
first differences.
6
6
8
11
The third differences
2
6
are constant.
14
9
16
7
x
y
The degree of the polynomial function is 3.
3
23
Got It?
4. a. What is the degree of the polynomial function that generates
2
16
the data shown at the right?
1
15
b.
Reasoning
What is an example of a polynomial function whose
0
10
fifth differences are constant but whose fourth differences are
not constant?
1
13
2
12
3
29
122
Honors Supplement
122
Common Core
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