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USING FINITE DIFFERENCES TO WRITE A FUNCTION

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.

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USING FINITE DIFFERENCES TO WRITE A FUNCTION

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  1. USING FINITE DIFFERENCES TO WRITE A FUNCTION Objective 1.03

  2. Important Definitions • Monomial: a number or a product of numbers and variables with whole number expressions.

  3. Important Definitions • Monomial: a number or a product of numbers and variables with whole number expressions. • Example:

  4. 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.

  5. 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:

  6. 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: • What is the degree of this polynomial? • Identify the exponent • Degree is 3

  7. FINITE DIFFERENCES OF POLYNOMIALS

  8. Example • The table to the right shows the population of a city from 1950 – 1980. • Write a polynomial for the data.

  9. Find Degree Using Finite Differences

  10. Find Degree Using Finite Differences 1000

  11. Find Degree Using Finite Differences 1000 2000

  12. Find Degree Using Finite Differences 1000 2000 3000

  13. Find Degree Using Finite Differences 1000 1000 2000 3000

  14. Find Degree Using Finite Differences 1000 1000 2000 1000 3000

  15. Find Degree Using Finite Differences 1000 1000 2000 1000 3000

  16. 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:

  17. 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:

  18. 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:

  19. 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

  20. 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

  21. Make a Prediction • Use your polynomial to tell me what the population will be in the year 2020.

  22. Make a Prediction • Use your polynomial to tell me what the population will be in the year 2020.

  23. Make a Prediction • Use your polynomial to tell me what the population will be in the year 2020. = 30,000 people in 2020

  24. 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.

  25. 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

  26. 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.

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