2/11 Alg2: Applications of Polynomials

2/11 Thursday

Algebra 2

Afternoon Message

Good afternoon! Happy Thursday :)

Yesterday we worked with operations on polynomials. Today we will see why this is useful in real life. Do you want to understand how to manage your profit for a business?

Announcements:

I have office hours today and for the rest of the week.

If you need to make up Friday's test, you can do so this Friday.

You have a 3-day weekend coming up :)

Complete all practice quizzes from Chapter 2 as makeup credit for any missing Quizizz assignment.

Agenda

• Learning Target

• Do Now Review

• Review of Yesterday

• Applications of Polynomials

• Debrief/Learning Target check-in

• Exit Ticket

Poll

Learning Target: I can apply my knowledge of polynomial functions to solve real-world problems.

Rate your current state of understanding of the learning target.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Kakegurui! Let's review the Do Now!

Poll

Which would you rather?

• Option A

• Option B

A Brief Review of Yesterday

Adding, Subtracting, Multiplying Polynomials

Let's try this together.

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Answer

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Applications of Polynomials

Businesses use polynomials A LOT!

That Wind Chime Money Though

Carolina makes wind chimes to sell at the local street market. As Carolina produces a greater number of wind chimes, she can lower the price per unit.

The function 𝙫(𝙭) = 𝟰𝟴 − 𝟮𝙭 relates the price v to the number produced x. The cost c of making x wind chimes can be represented with the function 𝙘(𝙭) = 𝟭𝟮𝙭 + 𝟲𝟰.

How many wind chimes should Carolina sell each week to maximize her profit P?

Multiple Choice

Subtract the polynomials to find the function for profit.

 $P\left(x\right)=\left(48-2x\right)x-\left(12x+64\right)$  

•  $P\left(x\right)=-2x^2+36x-64$  

•  $P\left(x\right)=34x+64$  

•  $P\left(x\right)=-2x^2+60x+64$  

Graph of Carolina's Profit

Interpret the graph and think to yourself: What is Carolina's maximum profit?

Multiple Choice

What is Carolina's maximum profit?

• $100

• $98

• $9

• $15

Multiple Choice

How many chimes per week should Carolina sell to maximize her profit?

• 2

• 9

• 15

• 20

Things change in business, and the business model must adapt.

What if the cost to make Carolina's wind chimes changes?

Multiple Choice

Subtract the polynomials to find the function for profit.

 $P\left(x\right)=\left(48-2x\right)x-\left(4x+42\right)$  

•  $P\left(x\right)=-2x^2+44x-42$  

•  $P\left(x\right)=34x+64$  

•  $P\left(x\right)=-2x^2+60x+64$  

Debrief

• Polynomials are used in many real-life situations

• Knowing how to manage operations on polynomials can help determine important business matters, such as maximizing profit.

Poll

Learning Target: I can apply my knowledge of polynomial functions to solve real-world problems.

Rate your current state of understanding of the learning target.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there.

• 1 - I don't understand, I need some more help.

Great work today! Move to Google Classroom and complete your exit ticket.

Enjoy your day! :)