Transcript 7.2 Polynomial Functions and Their Graphs

Classification of a Polynomial
Degree
Name
Example
n=0
constant
3
n=1
linear
5x + 4
n=2
quadratic
2x2 + 3x - 2
n=3
cubic
5x3 + 3x2 – x + 9
n=4
quartic
3x4 – 2x3 + 8x2 – 6x + 5
n=5
quintic
-2x5 + 3x4 – x3 + 3x2 – 2x + 6
Warm-up
Classify 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
cubic polynomial
d) 3x3 + 2x – x3 – 6x5
quintic trinomial
e) 2x + 5x7
7th degree binomial
3 2
f ) 2  7
x
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:
Give the Local
Maxima and Minima
Must use y to describe High and Low
On the graph above:
A local maximum: f(x) =
A local minimum: f(x) =
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:
A)
f ( x)  x2  3x  2
B) g ( x)  x4  4 x2  1
C)
h( x)  2 x3  4 x2  9
Now describe their end behavior.

x  , y  
A) x  , y 
B)
x  , y  
x  , y  
C)
x  , y  
x  , y  
Describe the Interval of
Increasing and Decreasing
Must use x to describe Left to Right
(Left to Right)
The graph is:
y
x
Increasing when ___________
Decreasing when _____________
Increasing when ___________
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
A) y  2x2  3x  4
B) y  3x3  2x  1
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
C) y   x4  2