Lesson | Practice | 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 Integrated Math 2 Unit 5 Lesson 5

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 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

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
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

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.

teacher
student
family

Unit 5, Lesson 5

How Many Solutions?

$Course Icon$

Integrated Math 2

Practice

Problem 1

Rewrite each equation so that the expression on one side could be graphed and the -intercepts of the graph would show the solutions to the equation.

Problem 2

Here are equations that define quadratic functions , and . Sketch a graph, by hand or using technology, that represents each equation.
Determine how many solutions each of , and has. Explain how you know.

Problem 3

Mai is solving the equation . She writes that the solutions are and . Han looks at her work and disagrees. He says that only is a solution. Who do you agree with? Explain your reasoning.

Problem 4

ForLesson 4: Solving Quadratic Equations with the Zero Product Property

If the equation is true, which is also true according to the zero product property?

Only .

Problem 5

ForLesson 3: Solving Quadratic Equations by Reasoning

Solve the equation .
Show that your solution or solutions are correct.

Problem 6

ForLesson 3: Solving Quadratic Equations by Reasoning

To solve the quadratic equation , Andre and Clare wrote the following:

Andre

Clare

Identify the mistake each student made.
Solve the equation, and show your reasoning.

Problem 7

Decide if each equation has 0, 1, or 2 solutions, and explain how you know.

Only .

or .

or .