Transcript Advanced Algebra II Notes 7.1 Polynomial Degree and Finite

Advanced Algebra II Notes 7.1 Polynomial
Degree and Finite Differences
Definition of a Polynomial:
an xn  an1xn1  ....a1x1  a0
(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.
y  ax  bx  c
2
When third differences are same the terms have a cubic
relationship.
y  ax3  bx2  cx  d
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
Number of
diagonals
y
3
4
5
6
7
8
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=
and check the accuracy of the answer.
in the calculator
Assignment:
page 364:
1 – 4, 6, 8