6.4 Graphing Polynomial Functions
Relative maximum
Relative minimum
Making a table to graph
Graph the function
f(x) = -x3 - 4x2 + 5
The graph will cross the x axis 3 or less times since the degree is 3.
x f(x)-4 5-3 -4-2 -3-1 20 51 02 -193 -584 -123
Making a table to graph
Graph the function
f(x) = -x3 - 4x2 + 5
The graph
crosses
the x axis
3 times
x f(x)-4 5-3 -4-2 -3-1 20 51 02 -193 -584 -123
Find the area where the function equals zero
f(x) = x4 – x3 - 4x2 + 1
Make a table
Find the area where the function equals zero
f(x) = x4 – x3 - 4x2 + 1
Make a table
x f(x)
( -2, 9)
( -1, -1)
( 0, 1)
(1, -3)
( 2, -7)
( 3, 19)
( 4, 129)
Find the area where the function equals zero
f(x) = x4 – x3 - 4x2 + 1Make a table
Where are the zeros?
between -2 and -1 - 1and 0 0 and 1 2 and 3
x f(x)
( -2, 9)
( -1, -1)
( 0, 1)
(1, -3)
( 2, -7)
( 3, 19)
( 4, 129)
What are the Relative Maximum or Relative Minimum
It is an area where the highest or lowest points happen.
We make a table.
Graph the points and look for the highest and lowest points.
What are the Relative Maximum or Relative Minimum
Make the table for
f(x) = x3 – 4x2 + 5x f(x)
( -2, -19)
(-1, 0)
( 0, 5)
( 1, 2)
( 2, -3)
( 3, -4)
( 4, 5)
( 5, 30)
What are the Relative Maximum or Relative Minimum
Make the table for
f(x) = x3 – 4x2 + 5
Relative Max
near x=0
Relative Min
near x = 3
.
x f(x)
( -2, -19)
(-1, 0)
( 0, 5)
( 1, 2)
( 2, -3)
( 3, -4)
( 4, 5)
( 5, 30)
Graph the function
Between what numbers are the zeros of the function?
Graph the function
Between what numbers are the zeros of the function?
Between
-7 and -6
-4 and -3
3 and 4
Graph the function
Between what numbers are the Relative Max. and Min.
of the function?Between -6 and -5 R. Min 0 and 2 R. Max
Homework
Page 356
# 13 – 25 odd
Homework
Page 356
# 14 – 26 even