5.7 Completing the SquareCh. 6 Notes Page 38 P38 6.1: Polynomial Functions

Polynomial Functions

Polynomial Function:

where n is a nonnegative integer and an,…,a0 are real numbers.

011

1 ...)( axaxaxaxP nn

nn

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.

457 xx xxxx 234 32 526 x

Simplify. Classify each result by the number of terms. *When multiplying like bases, add the exponents.

Classifying Polynomials

678 33 dd 93865 33 xxx

265 2 xx 211 xxx

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 10 15 20

y 10.1 2.8 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 Square6.1: Polynomial Functions

HW #35 6.1: P309 #1, 3, 4, 6, 13, 14, 18, 22, 39, 40, 46, 48