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