Functions Extrema

Lesson 3.5: A Field Guide to

Polynomial Functions

Obj: I can identify key features of a polynomial
function.

EQ: How do I describe characteristics of polynomial
functions?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Card Sort Activity

Desmos Card Sort

Go to https://student.desmos.com/join/3teuq4

Match each equation with its graph. Try matching
these without the use of a graphing utility. Record your
responses in your journal.

Match

Match each graph and formula.

f(x) = -x² - 2x - 6

f(x) = -2x³-4x²+5

f(x) = 1/20(x-3)(x+4)(x-5)

f(x) = (x+3)(x+2)²(x+5)

• f(x) = -x² - 2x - 6

• f(x) = -2x³-4x²+5

• f(x) = 1/20(x-3)(x+4)(x-5)

• f(x) = (x+3)(x+2)²(x+5)

Fill in the Blanks

What is the lowest possible degree of this function?

Multiple Choice

What is the end behavior of this graph?

• Down, Down

• Up, Up

• Up, Down

• Down, Up

• y = -5

Drag and Drop

Extrema: 1 ​

Placeholder

at ​

Placeholder

Zeros: ​

Placeholder

Y-int: ​

Placeholder

Drag these tiles and drop them in the correct blank above

maximum

minimum

y = -5

x = -1

No real zeros

(-6, 0)

(0, -6)

Fill in the Blanks

What is the lowest possible degree of this function?

Multiple Choice

What is the end behavior of this graph?

• Down, Down

• Up, Up

• Up, Down

• Down, Up

• y = 1

Drag and Drop

Extrema: ​

Placeholder

Y-int: ​

Placeholder

Drag these tiles and drop them in the correct blank above

(0, 5)

1 min, 1 max

2 min

2 max

(0, 1)

Fill in the Blanks

What is the lowest possible degree of this function?

Multiple Choice

What is the end behavior of this graph?

• Down, Down

• Up, Up

• Up, Down

• Down, Up

• y = 5

Drag and Drop

Extrema: ​

Placeholder

Zeros: ​​

Placeholder

Y-int: ​

Placeholder

Multiplicities: ​

Placeholder

for each factor

Drag these tiles and drop them in the correct blank above

2 max

2 min

(0, 3)

1 max, 1 min

{3, 5}

{-5, -3, 4}

{-4, 3, 5}

1

2

Fill in the Blanks

What is the lowest possible degree of this function?

Multiple Choice

What is the end behavior of this graph?

• Down, Down

• Up, Up

• Up, Down

• Down, Up

• y = -5

Drag and Drop

Extrema: ​

Placeholder

min, ​

Placeholder

max
Zeros: {​

Placeholder

, ​ -3 , -2}
Y-int: (0, 60)

Placeholder

; (x+2) is ​

Placeholder

Drag these tiles and drop them in the correct blank above

2

1

-5

5

-2

Part 2: Handout 3.5

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin
the wheel as a class and spend a minute or
so discussing our answers.