Transcript 9-3 - Finding Polynomial Models

9-3
4/6/2016
9-3
Finding
Polynomial
Models
9-3
4/6/2016
Determining Degree
Give me an
equation of a line
where the slope is a
whole number:
f(x) =
Give me a quadratic
equation with whole
numbers for A, B, & C:
f(x) =
Give me a 3rd degree
polynomial with whole
number coefficients:
f(x) =
x
1
2
3
4
5
6
1
2
3
4
5
6
1
2
3
4
5
6
f(x)
Diff:
x
f(x)
Diff:
2nd diff:
x
f(x)
Diff:
2nd diff:
3rd diff:
9-3
4/6/2016
Determining Degree
If you know a list of numbers comes from
a polynomial model, you can determine
the degree of the polynomial by:
• Find the difference between consecutive terms
• If the differences are the same, it is a linear
function (degree 1)
• If not, find the difference of the differences.
• Repeat until the differences are constant.
• The number of times you have to find the
difference is the degree of the polynomial.
9-3
4/6/2016
Determining Degree
x
1
2
3
4
5
6
f(x)
-14
2
36
130
350
786
Diff
2nd Diff
3rd Diff
4th Diff
The 4th Differences are constant so
these came from a 4th degree
polynomial
9-3
4/6/2016
Finding a Model
To find a polynomial
model:
x
1
2
3
4
f(x)
7
4
5
16
• Find the degree
• Enter data into lists in the
Calculator.
• To appropriate regression
to get model.
This is degree 3
a = 1 b = -4 c = 2 d = 8
f(x) = x3 – 4x2 + 2x + 8
9-3
4/6/2016
Application
Jeff thinks it would be fun to roll a marble down a hill and
record the distance away from him the marble goes
after each second. He records the following
information:
After 1 second, the marble was 1 inch away, after 2
seconds, it was 4 inches away, after 3 seconds, it was
10 inches away, after 4 seconds, it was 20 inches, and
after 5 seconds, it was 35 inches away. Something
caught Jeff’s attention after 5 seconds, and he was not
able to see how far away the marble was after 6
seconds. Find a model for this data so you can help
him figure it out.
9-3
4/6/2016
Things to be careful of:
The independent values in the table MUST
represent an arithmetic sequence. Remember,
we are looking for a CONSTANT difference.
The direction you take to find your differences must
remain consistent throughout the “row” of
differences. You can only change direction with a
new row of differences, not in the middle of the row
to keep the math “easier”.