USING FINITE DIFFERENCES
TO WRITE A FUNCTION
Objective 1.03
Important Definitions

Monomial: a number or a product of
numbers and variables with whole
number expressions.
Important Definitions

Monomial: a number or a product of
numbers and variables with whole
number expressions.
 Example:
x
3
Important Definitions

Monomial: a number or a product of
numbers and variables with whole
number expressions.
 Example:

x
3
Polynomial: a monomial or a sum or
difference of monomials.
Important Definitions

Monomial: a number or a product of
numbers and variables with whole
number expressions.
 Example:

x
3
Polynomial: a monomial or a sum or
difference of monomials.
 Example:
5 x  8 x  3x
3
2
Important Definitions

Monomial: a number or a product of
numbers and variables with whole
number expressions.
 Example:

Polynomial: a monomial or a sum or
difference of monomials.
 Example:

x
3
5 x  8 x  3x
3
2
What is the degree of this polynomial?
 Identify
the exponent
 Degree is 3
FINITE DIFFERENCES OF
POLYNOMIALS
FUNCTION TYPE
DEGREE
CONSTANT FINITE
DIFFERENCE
LINEAR
1
FIRST
QUADRATIC
2
SECOND
CUBIC
3
THIRD
QUARTIC
4
FOURTH
QUINTIC
5
FIFTH
Example


The table to the right
shows the population
of a city from 1950 –
1980.
Write a polynomial
for the data.
X
Y
1950
2000
1960
3000
1970
5000
1980
8000
Find Degree Using Finite Differences
X
Y
1950
2000
1960
3000
1970
5000
1980
8000
Find Degree Using Finite Differences
X
Y
1950
2000
1000
1960
3000
1970
5000
1980
8000
Find Degree Using Finite Differences
X
Y
1950
2000
1000
1960
3000
2000
1970
5000
1980
8000
Find Degree Using Finite Differences
X
Y
1950
2000
1000
1960
3000
2000
1970
5000
3000
1980
8000
Find Degree Using Finite Differences
X
Y
1950
2000
1000
1960
1000
3000
2000
1970
5000
3000
1980
8000
Find Degree Using Finite Differences
X
Y
1950
2000
1000
1960
1000
3000
2000
1970
5000
1000
3000
1980
8000
Find Degree Using Finite Differences
X
Y
1950
2000
1000
1960
1000
3000
2000
1970
5000
1000
3000
1980
8000
What is the degree of our polynomial
going to be?




How many steps did we take to get to a constant
difference?
It took us 2 columns of differences to get to 1000.
So the degree is 2.
Our polynomial will look something like this:
What is the degree of our polynomial
going to be?




How many steps did we take to get to a constant
difference?
It took us 2 columns of differences to get to 1000.
So the degree is 2.
Our polynomial will look something like this:
__ x  ___ x  ___
2
What is the degree of our polynomial
going to be?




How many steps did we take to get to a constant
difference?
It took us 2 columns of differences to get to 1000.
So the degree is 2.
Our polynomial will look something like this:
ax  bx  c
2
Using Graphing Calculator






Click Stat
 Choose Edit
Put the x values in List 1
Put the f(x) values in List 2
Click 2nd
 Click quit
Click Stat
 Choose Calc
Choose proper function
 Quadratic
Using Graphing Calculator






Click 2nd
 Click Stat
Put the x values in List 1
Put the f(x) values in List 2
Click 2nd
 Click quit
Click Stat
 Calc
Choose proper function
 Quadratic
5x  19450x  1891700
2
Make a Prediction

Use your polynomial to tell me what the population
will be in the year 2020.
Make a Prediction

Use your polynomial to tell me what the population
will be in the year 2020.
5(2020)  19450(2020)  18917000
2
Make a Prediction

Use your polynomial to tell me what the population
will be in the year 2020.
5(2020)  19450(2020)  18917000
2
= 30,000 people in 2020
Your Turn!


In your groups, use what you have learned to create
a polynomial from the given information.
Use your polynomial to make the prediction.
Pictures Came From

http://www.flickr.com/photos/moomoo/2462069317/

http://commons.wikimedia.org/wiki/File:TI-84_Plus.jpeg

http://www.flickr.com/photos/64281135@N00/54335576

http://school.discoveryeducation.com/clipart/clip/pyramids.html

http://jwilson.coe.uga.edu/emt668/EMAT6680.2004.SU/Bird/emat6690/trapezoid/trapezoid.html

http://jwilson.coe.uga.edu/emt668/EMAT6680.2004.SU/Bird/emat6690/trapezoid/trapezoid.html

http://www.free-clipart-of.com/FreeBasketballClipart.html
Works Cited

Burger, E.B., Chard, D.J., Hall, E.J., Kennedy, P.A., Leinwand, S.J.,
Renfro, F.L., Seymour, D.G., & Waits, B.K. (2011). Algebra 2
(teachers edition). Orlando: Houghton Mifflin Publishing
Company.