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