LESSON
Reteach
Curve Fitting with Polynomial Models
To use finite differences to determine the degree of a polynomial,
− check that the x-values increase by a constant value, and
− find successive differences of the y-values until the differences are
constant.
Example:
A fourth degree polynomial best describes the data.
Use finite differences to determine the degree of the polynomial that best describes the data.
1.
|x |(2 |(1 |0 |1 |2 |
|y |(5 |2 |3 |4 |11 |
|First Differences | |
|Second Differences | |
|Third Differences | |
2. Identify the degree of the polynomial.
Reteach
Curve Fitting with Polynomial Models (continued)
Use finite differences that are close to select a polynomial model to fit a data set. Then use your calculator to write the function.
Since the third differences are reasonably close, you can
use a cubic function to model the data.
Use the cubic regression feature on your calculator.
Use the coefficients a, b, c, and d to write the function.
f(x) ( 0.12x 3 ( 8.06x 2 ( 273.1x ( 584.6
Write a polynomial function for the data.
3.
|x |2 |4 |6 |8 |10 |12 |
|y |(12 |(15 |38 |190 |446 |773 |
|First Differences | |
|Second Differences | |
|Third Differences | |
|Fourth Differences | |
4. Write a polynomial function that best describes the data set.
-----------------------
LESSON
6-9
|Finite Differences |
|Function Type |Linear |Quadratic |Cubic |Quartic |Quintic |
|Degree |1 |2 |3 |4 |5 |
|Constant Finite Differences |First |Second |Third |Fourth |Fifth |
|x |(3 |(2 |(1 |0 |1 |2 |
|y |78 |14 |0 |0 |2 |18 |
|First Differences |14 ( 78 |0 ( 14 |0 ( 0 |2 ( 0 |18 ( 2 |
| |(64 |(14 |0 |2 |16 |
|Second Differences |(14 ( ((64) |0 ( ((14) |2 ( 0 |16 ( 2 |
| |50 |14 |2 |14 |
|Third Differences |14 ( 50 |2 ( 14 |14 ( 2 |
| |(36 |(12 |12 |
|Fourth Differences |(12 ( ((36) |12 ( ((12) |
| |24 |24 |
The x-values increase by 1.
First differences are not constant.
Second differences are not constant.
Third differences are not constant.
Fourth differences are constant.
LESSON
6-9
|x |10 |20 |30 |40 |50 |
|y[?] ª ¬ |2633 |3812 |4862 |6529 |9552 |
|#$&'*+ÅÆÇÈÊËÓÔÕÖ×âãôö| | | | | |
|÷ | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
|K | | | | | |
|N | | | | | |
|O | | | | | |
|| | | | | | |
|‡ | | | | | |
|ˆ | | | | | |
|ÇÈÊËÍÎÔÕîïðñòóðìæìæìð| | | | | |
|ìðìðìðìðìðìàìÙìÙìÓàìÙ| | | | | |
|ìÓÍìÓÍìÓÍìÓìÈðì»ìðìð| | | | | |
|ìæìæìæìæìæ°æ§ìh6Û0J6?| | | | | |
|]?h6Û0J6?EH[?] | | | | | |
|First Differences |3812 ( 2633 |4862 ( 3812 |6529 ( 4862 |9552 ( 6529 |
| |1179 |1050 |1667 |3023 |
|Second Differences |1050 ( 1179 |1667 ( 1050 |3023 ( 1667 |
| |(129 |617 |1356 |
|Third Differences |617 ( ((129) |1356 ( 617 |
| |746 |739 |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- water theme preschool lesson plans
- lesson plans high school history
- lesson plans for us history
- lesson plans for kindergarten
- lesson plan themes by month
- preschool lesson on water
- water lesson plan for preschoolers
- living water lesson for kids
- free printable english lesson worksheets
- water lesson plans for toddlers
- free lesson plans for english
- water lesson plans pre k