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 nonreal 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 \(b^24ac\), building on some of the thinking in the previous lesson where students used the quadratic formula to find nonreal solutions to quadratic equations.
It is especially beneficial for each student or pair of students to have access to graphing technology for this lesson.
Lesson overview
 19.1 Warmup: Notice and Wonder: Where Is It 0? (5 minutes)
 19.2 Optional Activity: Real or Not? (15 minutes)
 19.3 Optional Activity: Make Your Own (15 minutes)

Lesson Synthesis
 There is a digital applet to support discussion in this synthesis.
 19.4 Cooldown: Make it Complex (5 minutes)
Learning goals:
 Create quadratic equations that will have either real or nonreal solutions, then calculate the specific solutions.
 Justify that a quadratic equation will have either real or nonreal solutions using graphical reasoning.
Learning goals (student facing):
 Let's create and solve quadratic equations.
Learning targets (student facing):
 I can find complex solutions to quadratic equations.
Standards:
 This lesson builds towards the standard: CCSS.HSAREI.B.4.bMS.AREI.4bMO.A1.REI.A.2c
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