Advanced Algebra II Notes 7.1 Polynomial Degree and Finite Differences

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Presentation transcript:

Advanced Algebra II Notes 7.1 Polynomial Degree and Finite Differences Definition of a Polynomial: (exponents are nonnegative integers) (coefficients are real) Degree of polynomial: Power of terms with greatest exponent. Degree of term: Sum of exponents of variable factors in the term. General form: Descending power of variables. Monomial: single term Binomial: two terms Trinomial: three terms

First differences (D1 ) second differences ( D2) and third differences ( D3) When first differences are same the terms have a linear relationship. y = mx + b When second differences are same the terms have a quadratic relationship. When third differences are same the terms have a cubic relationship.

Find a polynomial function that models the relationship between the number of sides and the number of diagonals of a polygon. Use the function to find the number of diagonals of a dodecagon. Number of sides x 3 4 5 6 7 8 Number of diagonals y

Using a motion detector (Ranger), an Algebra II class collected the following data for the height of an object dropped from 2 meters. Time (s) x Height (m) y 0.00 2.000 0.05 1.988 0.10 1.951 0.15 1.890 0.20 1.804 0.25 1.694 0.30 1.559 0.35 1.400 0.40 1.216 0.45 1.008

1. Use the finite differences method to determine the degree of the polynomial function that models this data. 2. Enter the data into List 1 (x) and List 2 (y). Graph the relationship as a scatter plot. 3. Choosing the correct model, write a system of equations and solve. 4. Write the equation of the model, put it into y= in the calculator and check the accuracy of the answer.

Assignment: page 364: 1 – 4, 6, 8