# 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.

### Student Facing

• I can find complex solutions to quadratic equations.