Navigation

9-12 Integrated Math 2 Unit 6 Lesson 13

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

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
Unit 8

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 | 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.

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

Unit 6, Lesson 13

Completing the Square and Complex Solutions

$Course Icon$

Integrated Math 2

Practice

Problem 1

Find the complex solutions to each equation.

\(x^2+0.5x-14=0\)
\(x^2+12x+36=0\)
\(x^2-3x+8=0\)
\(x^2+4=0\)

Problem 2

Which describes the solutions to the equation \(x^2+7=0\)?

One real solution
Two real solutions
One non-real solution
Two non-real solutions

Problem 3

ForLesson 8: Inequivalent Equations?

Explain how you know \(\sqrt{3x+2}=\text-16\) has no solutions.

Problem 4

Use the graphs to determine the number of real solutions and non-real solutions to each equation. The types of solutions can be found without doing any calculations.

\(x^2-6x+7=0\)
\(3x^2+2x+1=0\)
\(\text-x^2-3x+2=0\)
\(x^2-6x+7=\text-2\)
\(\text-x^2-3x+2=6\)
\(3x^2+2x+1=2\)

<p>Parabola y= x squared -6x +7.</p> — \(y=x^2-6x+7\)

<p>Parabola y= 3 x squared +2x + 1.</p> — \(y=3x^2+2x+1\)

<p>Parabola y= - x squared -3x +2.</p> — \(y=\text-x^2 - 3x +2\)

Problem 5

ForLesson 11: More Arithmetic with Complex Numbers

Write \((5-5i)^2\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers.
Write \((5-5i)^4\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers.