Math 3Name______

3-3Zeroes & Factors of Polynomials (Part 2)

Learning Goals:

  • I understand the relationship between local minimum and local maximum, absolute maximum and absolute minimum.
  • I understand the value of ordered pair is implied to be the y-value.

1.Another important characteristic of polynomials is the absolute (or global) maximum and minimum values and the local (or relative) maximums and minimum values. See both illustrated below.

2a.What is the difference between a local minimum and an absolute minimum?

2b.Why does the graph NOT have an absolute maximum?

2c.In your own words, write a definition of a local minimum/maximum.

Check your answer with your teacher before you move on!

2d.Note that in the above graph, is an absolute minimum pointof f, and

What is the minimum value? Hint: re-read the learning goal.

2e.Use your calculator to find the local maximum value of f.

2f.Use your calculator to find the local minimum value of f.

3.Use the function below to answer the following questions. You are not given an equation so estimate from the graph!

  1. At what point is there a local maximum?
  1. What is the local maximum value?
  1. At what point is there a local minimum?
  1. What is the local minimum value?
  1. State the coordinates of the local minimum.
  1. What do you know about the degree and the leading coefficient of the equation of the above function?
  1. Explain why the graph does NOT have an absolute maximum or absolute minimum.
  1. Generalize your answer – what types of polynomials will have absolute maximum or minimums and what types will not?

Related to the maximums and minimums of a polynomial function is how often the functions change direction (from increasing to decreasing or vice versa).

4.What is the degree of a parabola? ______

How many times does the graph of a parabola change directions?______

How many maximums and/or minimums (global or local) does a parabola have? ______

5.What is the end behavior of a 3rd degree polynomial? Sketch an example to the right.

How many times does the graph of your 3rd degree polynomial change direction? ______

How total many max/mins (global or local) does the 3rd degree polynomial have?______

6.What is the degree of ?______

Sketch an example to the right (change your x-axis window to ).

Graph on your calculator. How many times does it change direction? ______

How many total maximums and/or minimums (global or local) doeshave ? ______

7.What is the degree of ?______

Sketch an example to the right (change your x-axis window to ).

How many total maximums and/or minimums (global or local) does have? ______

8.What is the degree of ?______

Sketch it below (change your x-axis window to )

How many maximums and/or minimums (global or local) does have? ______

9.What is the relationship between the degree of a graph and the number of total maximums and/or minimums (local and global combined)?