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.

Navigation

9-12 Algebra 1 Unit 8 Lesson 3

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

•Algebra 1 Geometry Algebra 2 Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 •Unit 8

Modeling Prompts

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 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23 Lesson 24

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

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 16
Lesson 17
Lesson 18
Lesson 19
Lesson 20
Lesson 21
Lesson 22
Lesson 23
Lesson 24

Settings

Language

Audience

family

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.

English
Español

teacher
student
family

Lesson 3

3.1 Warm-up 3.2 Activity Student Lesson Summary

Unit 8, Lesson 3

Solving Quadratic Equations by Reasoning

Algebra 1

3.1

Warm-up

How Many Solutions?

How many solutions does each equation have? What are the solution(s)? Be prepared to explain how you know.

Are You Ready for More?

3.2

Activity

Finding Pairs of Solutions

Standards Alignment

Building On

Addressing

A-REI.4.b

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

View Full Standard

Building Toward

Each of these equations has two solutions. What are they? Explain or show your reasoning.

Are You Ready for More?

Student Lesson Summary

Some quadratic equations can be solved by performing the same operation on each side of the equal sign and reasoning about which values for the variable would make the equation true.

Suppose we wanted to solve . We can proceed like this:

Add 75 to each side:

Divide each side by 3:

What number can be squared to get 25?

There are two numbers that work, 5 and -5:

and

If , then .
If , then .

This means that both and make the equation true and are solutions to the equation.

Many quadratic equations have 2 solutions, but some have only 1 or no solution.

Glossary

None

Have feedback on the curriculum?

Help us improve by sharing suggestions or reporting issues.

Submit Feedback

Standards Alignment

Building On

Addressing

A-REI.1

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

View Full Standard

A-REI.4.b

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

View Full Standard

Building Toward