### 5.8 Polynomial Models in the Real World

```2/11/2014
Tuesday, 2/11
You Need:
Clickers!
Fancy Calculators
Possibly textbooks
On your desk to be checked during bellwork:
Pg. 329 #8,21,22,24,26-30,45,48,49
1
2/11/2014
Chapter 5 Test:
Either the 17th and 18th
(Monday and Tuesday)
or
th
18 and block day (19th or 20th)
Tuesday and Wed/Thur.
Questions on homework will be taken
at the end of class.
19
5.8 Polynomial Models in the
Real World
(n+1) Point Principle
For any set of n+1 points in the coordinate plane that
pass the vertical line test, there is a unique polynomial
of degree at most n that fits the points perfectly.
(n+1) Point Principle
For any set of n+1 points in the coordinate plane that
pass the vertical line test, there is a unique polynomial
of degree at most n that fits the points perfectly.
Meaning: Any two points determine a unique line.
Three points that are not on a line determine a unique
parabola. Four points that are not on a line or a
parabola determine a unique cubic, etc.
2
2/11/2014
Example 1:
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
By the (n+1) point principle, there is a _________
polynomial that fits the points perfectly.
Example 1:
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
By the (n+1) point principle, there is a __cubic__
polynomial that fits the points perfectly.
By the (n+1) point principle, there is a __cubic__
polynomial that fits the points perfectly.
Open a Lists and Spreadsheets Document
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
By the (n+1) point principle, there is a __cubic__
polynomial that fits the points perfectly.
By the (n+1) point principle, there is a __cubic__
polynomial that fits the points perfectly.
Open a Lists and Spreadsheets Document
Open a Lists and Spreadsheets Document
Remember, you
MUST name your
lists, even if it is
just “x” and “y”.
3
2/11/2014
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
By the (n+1) point principle, there is a __cubic__
polynomial that fits the points perfectly.
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
By the (n+1) point principle, there is a __cubic__
polynomial that fits the points perfectly.
Click “ctrl” and “doc” (to add a page)
Add a Data and Statistics Page
Click “ctrl” and “doc” (to add a page)
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
Click each
axis to select
the title of
your list for
each one.
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
4: Analyze
6: Regression
5: Show Cubic
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
Click each
axis to select
the title of
your list for
each one.
Example 1:
What polynomial function has a graph that passes through
the four points (0,-3), (1,-1),(2,5), and (-1,-7)?
4: Analyze
6: Regression
5: Show Cubic
4
2/11/2014
Which of the two
graphs below do you
think accurately
describes the realworld situation?
Extrapolation and Interpolation
Interpolation: Estimating within the given domain (usually
using an equation).
Extrapolation: Estimating outside the given domain (using
an equation).
Interpolation is more reliable. Extrapolation
becomes less and less reliable the farther you
move from the data.
Use year 0 for 1900!
5
2/11/2014
Questions on homework ?
We would have the least amount of confidence
in 2012 because it is not within our original
data.
HW: Pg. 335 #10,12,14,16-23, 28, 33,
36
6
```