7.2 Graphing Polynomial Functions

1
7.2 Graphing Polynomial Functions

• Relative maximum
• Relative minimum

2
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.

3
Making a table to graph

• Graph the function
• f(x) -x3 - 4x2 5
• The graph
• crosses
• the x axis
• 3 times

4
Find the area where the function equals zero

• f(x) x4 x3 - 4x2 1
• Make a table

5
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)
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Find the area where the function equals zero

• f(x) x4 x3 - 4x2 1
• Make 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)
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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.

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What are the Relative Maximum or Relative Minimum

• Make the table for
• f(x) x3 4x2 5

x f(x)
( -2, -19)
(-1, 0)
( 0, 5)
( 1, 2)
( 2, -3)
( 3, -4)
( 4, 5)
( 5, 30)
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What are the Relative Maximum or Relative Minimum

• Make the table for
• f(x) x3 4x2 5
• between
• -1 and 1
• Relative Max
• between
• 2 and 3
• Relative Min.

x f(x)
( -2, -19)
(-1, 0)
( 0, 5)
( 1, 2)
( 2, -3)
( 3, -4)
( 4, 5)
( 5, 30)
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Graph the function

• Between what numbers are the zeros of the
  function?

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Graph the function

• Between what numbers are the zeros of the
  function?
• Between
• -7 and -6
• -4 and -3
• 3 and 4

12
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

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Homework

• Page 356
• 13 25 odd

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Homework

• Page 356
• 14 26 even