Classification of a Polynomial

Degree Name Example

-2x5 + 3x4 – x3 + 3x2 – 2x + 6

n = 0

n = 1

n = 2

n = 3

n = 4

n = 5

constant 3

linear 5x + 4

quadratic 2x2 + 3x - 2

cubic 5x3 + 3x2 – x + 9

quartic 3x4 – 2x3 + 8x2 – 6x + 5

quintic

Warm-upClassify each polynomial by degree and by number of terms.

a) 5x + 2x3 – 2x2 cubic trinomial

b) x5 – 4x3 – x5 + 3x2 + 4x3

quadratic monomial

c) x2 + 4 – 8x – 2x3

d) 3x3 + 2x – x3 – 6x5

cubic polynomial

quintic trinomial

e) 2x + 5x7 7th degree binomial

2

3 2) 7fx x

Not a polynomial

Polynomial Graphs

Short Quiz: Tomorrow 1/27/10 (maybe)

Polynomial Functions and Their Graphs

There are several different elements to examine on the graphs of polynomial functions:

Local minima and maxima:

On the graph above: A local maximum: f(x) = A local minimum: f(x) =

Give the Local Maxima and Minima

Must use y to describe High and Low

Finding a local max and/or local min is EASY with the calculator!

Graph each of the following and find all local maxima or minima:

2) ( ) 3 2A f x x x 4 2) ( ) 4 1B g x x x 3 2) ( ) 2 4 9C h x x x

Now describe their end behavior.

yxA ,) ,x y

) ,B x y ,x y

) ,C x y ,x y

Describe the Interval of Increasing and Decreasing

Increasing when ___________

Decreasing when _____________

Increasing when ___________

Must use x to describe Left to Right

x

y

(Left to Right) The graph is:

Give the maximums and minimums and describe the intervals of increasing and decreasing, for each of the following:

Give the maximum and minimums and describe the intervals of increasing and decreasing, for each of the following:

Now, let’s do it on our own:For each of the following:

• sketch the graph• find the points at which there is a local max or min• describe the intervals in which the function is increasing or decreasing• describe the end behavior

2) 2 3 4A y x x 3) 3 2 1B y x x

4) 2C y x

Now, let’s do it on our own:For each of the following:

• sketch the graph• find the points at which there is a local max or min• describe the intervals in which the function is increasing or decreasing• describe the end behavior