In the previous lesson, students completed the square to find real and nonreal solutions to quadratic equations. In this lesson, students use the quadratic formula to calculate real and nonreal 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).
Lesson overview
 18.1 Warmup: Math Talk: Real or Not? (5 minutes)

18.2 Activity: Be Discriminating (15 minutes)
 Includes "Are you Ready for More?" extension problem
 18.3 Activity: Solving All Kinds of Quadratics (15 minutes)
 Lesson Synthesis
 18.4 Cooldown: Solve This Quadratic (5 minutes)
Learning goals:
 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 nonreal when using the quadratic formula.
Learning goals (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.
Standards:
 This lesson builds on the standard: CCSS.HSAREI.B.4MS.AREI.4bMO.A1.REI.A.2c
 This lesson builds towards the standard: CCSS.HSNCN.C.7MS.NCN.7MO.A2.REI.A.1
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