In this lesson, students apply what they learned about transforming expressions into factored form to make sense of quadratic equations and persevere in solving them (MP1). They see that rearranging equations so that one side of the equal sign is 0, rewriting the expression in factored form, and then using the zero product property make it possible to solve equations that they previously could only solve by graphing. These steps also allow them to easily see—without graphing and without necessarily completing the solving process—the number of solutions that the equations have.
Lesson overview
 9.1 Warmup: Why Would You Do That? (10 minutes)

9.2 Activity: Let’s Solve Some Equations! (15 minutes)
 Includes "Are you Ready for More?" extension problem
 9.3 Activity: Revisiting Quadratic Equations with Only One Solution (10 minutes)
 Lesson Synthesis
 9.4 Cooldown: Conquering More Equations (5 minutes)
Learning goals:
 Recognize that the number of solutions to a quadratic equation can be revealed when the equation is written as \(\text {expression in factored form} = 0\).
 Use factored form and the zero product property to solve quadratic equations.
Learning goals (student facing):
 Let’s solve some quadratic equations that before now we could only solve by graphing.
Learning targets (student facing):
 I can rearrange a quadratic equation to be written as \(\text {expression in factored form} = 0\) and find the solutions.
 I can recognize quadratic equations that have 0, 1, or 2 solutions when they are written in factored form.
Required materials:
 Graphing technology
Required preparation:
 Acquire devices that can run Desmos (recommended) or other graphing technology.
 It is ideal if each student has their own device. (Desmos is available under Math Tools.)
Standards:
 This lesson builds on the standard: CCSS.HSAREI.B.4.bMS.AREI.4bMO.A1.REI.A.2c
 This lesson builds towards the standard: CCSS.HSAREI.B.4MS.AREI.4MO.A1.REI.A.2c
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