Navigation

9-12 Integrated Math 3 Unit 2 Lesson 14

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 Integrated Math 2 •Integrated Math 3

Unit

Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 •Lesson 14 Lesson 15

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15

Lesson | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 4.0.

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Lesson 14

14.1 Warm-up 14.2 Activity 14.3 Activity Student Lesson Summary

Unit 2, Lesson 14

What Do You Know about Polynomials?

$Course Icon$

Integrated Math 3

14.1

Warm-up

is a polynomial. Here are some things we know about it:

It has degree 3.
Both and are factors of .
It has 2 horizontal intercepts, but only 1 is negative.
Its leading coefficient is negative.

What else do we know is true about ?

14.2

Activity

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

Silently read your card, and think about what information you need to answer the question.
Ask your partner for the specific information that you need. “Can you tell me ?”
Explain to your partner how you are using the information to solve the problem. “I need to know because .”

Continue to ask questions until you have enough information to solve the problem.
Once you have enough information, share the problem card with your partner, and solve the problem independently.
Read the data card, and discuss your reasoning.

If your teacher gives you the data card:

Silently read your card. Wait for your partner to ask for information.
Before telling your partner any information, ask, “Why do you need to know ?”
Listen to your partner’s reasoning, and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!

These steps may be repeated.
Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
Share the data card, and discuss your reasoning.

14.3

Activity

Without letting your partner see, do the following:
1. Write a polynomial of degree 3 or 4 in factored form.
2. Sketch the graph of your polynomial.
3. Rewrite its expression in standard form.
On a separate slip of paper, write the standard form of your polynomial along with one of the factors if the polynomial has degree 3, or two factors if the polynomial has degree 4. Trade slips with your partner.
Use the information your partner gave you about their polynomial to:
1. Rewrite their polynomial in factored form.
2. Sketch a graph of their polynomial, showing all horizontal intercepts.
Once you and your partner have finished graphing, check your factored form and graph with your partner, and discuss any differences.

Student Lesson Summary

We can look at the same polynomial in many different ways. Let’s think about . It’s written in standard form, but we could also write it in factored form as . If we graph , we get this:

<p>Coordinate plane, x, negative 4 to 4 by 1, y, negative 15 to 12 by 3. Curve begins near negative 4 comma negative 15, through negative 3 comma 0, 0 comma 6, 1 comma 0, 2 comma 0, toward 3 comma 12.</p>

Depending on what we know about and what we want to do, different forms will be more useful.

If we want to quickly estimate the value of for some value of , the graph might be most helpful.
If we don’t know what the graph of looks like, the factored form can help us find the zeros and sketch it.
If we want to know the general shape of the graph, we can use the standard form to find the end behavior.
If we want to know the factors of and we know only the standard form, we can guess some possible factors and divide by them.
If we have the factored form and we want to know the standard form, we can multiply all the factors together.

None