based on the dominant term, what is the end behavior of thi

1
Warm-up

• Find the zeros of this quadratic function by
  factoring
• x3 8x2 16x 0
• How many zeros does it have?

2
Todays Topics

• Section 2-3B High-Degree Polynomials
• Zeros of Polynomials

3
Finding Zeros

• What is a zero of a polynomial?
• What are the zeros of the following polynomial?

4
Finding Zeros

• Sometimes, when a polynomial equation is factored
  it contains a perfect square or perfect cube
  factor.
• When a zero is repeated, we say that the zero has
  a multiplicity.
• (x 3)2 0 The zero x 3 has a multiplicity
  of 2
• (x 1)5 0 The zero x -1 has a
  multiplicity of 5

5
Finding Zeros

• The multiplicity of a zero tells us something
  about the graph of the function
• Even multiplicity the graph touches the x-axis
  but doesnt cross it (the zero is a local max or
  min of the function)
• Odd multiplicity the function crosses the x-axis
  at this point.

6
Finding Zeros

• Confirm the rule for this function that has been
  completely factored
• What would be the degree of the dominant term in
  this function if it were expanded?
• Based on the dominant term, what is the end
  behavior of this function?

7
Example 1

• Use your knowledge of end behavior and
  multiplicity of zeros to make a rough sketch of
  this function without a calculator
• f(x) x(x 6)2
• (Whats the total degree of the dominant term?)

8
Example 2

• Use your knowledge of end behavior and
  multiplicity of zeros to make a rough sketch of
  this function without a calculator
• f(x) -.02x(x 3)2(x 5)2
• (Whats the total degree of the dominant term?)

9
Example 3

• Find a cubic function with the following zeros
• zeros x -2, 1, 4

10
Example 4

• Find a cubic function with the following zeros
• zeros x

11
Homework Assignment

• Get started on Section 2-3B homework
• p. 210 33,38,39,42,45-57 odd, 63