Lesson 19

Real and Non-Real Solutions

Lesson Narrative

This lesson is optional practice that not all classes may need. Students begin by predicting how many real solutions a quadratic equation will have. Next, they create, and solve, their own quadratic equations that have either real or non-real solutions. To do this, they will need to see and make use of the structure of quadratic equations (MP7). A focus of this work is on the value of \(b^2-4ac\), building on some of the thinking in the previous lesson where students used the quadratic formula to find non-real solutions to quadratic equations.

It is especially beneficial for each student or pair of students to have access to graphing technology for this lesson.


Learning Goals

Teacher Facing

  • Create quadratic equations that will have either real or non-real solutions, then calculate the specific solutions.
  • Justify that a quadratic equation will have either real or non-real solutions using graphical reasoning.

Student Facing

Let's create and solve quadratic equations.

Learning Targets

Student Facing

  • I can find complex solutions to quadratic equations.

CCSS Standards

Addressing

Building Towards

Print Formatted Materials

Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.

Student Task Statements pdf docx
Cumulative Practice Problem Set pdf docx
Cool Down Log In
Teacher Guide Log In
Teacher Presentation Materials pdf docx

Additional Resources

Google Slides Log In
PowerPoint Slides Log In