# Lesson 18

The Quadratic Formula and Complex Solutions

### Lesson Narrative

In the previous lesson, students completed the square to find real and non-real solutions to quadratic equations. In this lesson, students use the quadratic formula to calculate real and non-real solutions.

Students construct viable arguments and critique the reasoning of others when they compare solutions of equivalent quadratic equations and resolve any disagreements during a row game (MP3).

### Learning Goals

Teacher Facing

- Calculate complex solutions using the quadratic formula and represent them in the form $c \pm di$, where $c$ and $d$ are real numbers.
- Explain reasoning and critique the reasoning of others when solving quadratic equations.
- Explain when solutions are non-real when using the quadratic formula.

### Student Facing

- Let’s use the quadratic formula to find complex solutions to quadratic equations.

### Learning Targets

### Student Facing

- I can find complex solutions to quadratic equations by using the quadratic formula.