Transcript Degree of a Polynomial

5.7 Completing
the
Square
Ch. 6 Notes Page 38
P38 6.1: Polynomial Functions
Polynomial Functions
n
n 1
P
(
x
)

a
x

a
x
 ...a1 x  a 0
Polynomial Function:
n
n 1
where n is a nonnegative integer and an,…,a0 are real numbers.
Degree: the exponent of a variable
Standard Form of a Polynomial: Terms in descending order by
degree
Degree of a Polynomial: The largest degree of any term in the
polynomial
***The degree of a polynomial tells us how many zeros the function
has!!!
Classifying Polynomials
Classifying Polynomials
Write each polynomial in standard form. Then classify by
degree, name and number of terms.
 7 x  5x 4
x 2  4 x  3x 3  2 x
6  2 x5
Classifying Polynomials
Simplify. Classify each result by the number of terms.
*When multiplying like bases, add the exponents.
 8d
3
 
7   d3 6
5 x 6 x  2 
2

5x
3
 
 6 x  8  3x 3  9
x  1x 1x  2

Comparing Models
Using a calculator, determine whether a linear, quadratic, or cubic
function would best fit the values in the table.
**We will need to plot the points and the function on the calc!
x
0
5
y
10.1 2.8
10
15
20
8.1
16.0 17.8
Real Life
The table shows gold production for several years. Find a quartic
function to model the data. Use it to estimate production of gold in
1988.
Year
1975
1980
1985
1990
1995
2000
Production
(millions of
ounces)
38.5
39.2
49.3
70.2
71.8
82.6
5.7
Completing
the
Square
6.1: Polynomial Functions
HW #35 6.1: P309 #1, 3, 4, 6, 13, 14, 18, 22,
39, 40, 46, 48