3.5 Lesson: Extrema with Absolutes and Relative

Extrema and
End Behavior

By Blake Jensen with Credit to McGraw Hill

Open Ended

In your own words, what do you think extrema means?
It's okay to guess!

Extrema means......

Extremes!

Used to talk about maximums and minimums.

Multiple Choice

Do you think this graph has a maximum or a minimum?

• Maximum

• Minimum

The graph to the right has an absolute minimum.

This means it has a point that is the lowest on the graph.

The place at which it occurs is 1

It's value is -4

​

Absolutes

Drag and Drop

​ ​ The following has an absolute minimum.
The place at which it occurs is ​

Placeholder

The value of the minimum is​

Placeholder

Drag these tiles and drop them in the correct blank above

3

1

7

-2

8

Above the graph has an absolute minimum at a.

Do you think it has any other special points?

Absolute minimums

Relative minimums and relative maximums occur in spots where they look like a maxi or min but are not the highest or lowest point overall.

Relative Extrema

The highest point on the graph overall.

Absolute Maximums

Multiple Choice

True or false

This graph has no absolute minimums or maximums.
(Assume there are arrows on the ends of the graph)

• True

• False

Labelling

Label each of the following with their correct vocab word.
Assume this is the full graph

Drag labels to their correct position on the image

Absolute Maximum

Relative maximum

Relative Minimum

Absolute minimum