In this lesson, students return to some quadratic functions they have seen. They write quadratic equations to represent relationships and use the quadratic formula to solve problems that they did not previously have the tools to solve (other than by graphing). In some cases, the quadratic formula is the only practical way to find the solutions. In others, students can decide to use other methods that might be more straightforward (MP5).
The work in this lesson—writing equations, solving them, and interpreting the solutions in context—encourages students to reason quantitatively and abstractly (MP2).
Lesson overview
 17.1 Warmup: No Solutions for You! (5 minutes)
 17.2 Activity: The Potato and the Pumpkin (15 minutes)

17.3 Activity: Back to the Framer (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 17.4 Cooldown: Tennis Ball Up, Tennis Ball Down (5 minutes)
Learning goals:
 Interpret (orally and in writing) the solutions to quadratic equations in context.
 Practice using the quadratic formula to solve quadratic equations, rearranging the equations into \(ax^2+bx+c=0\) if not already given in this form.
Learning goals (student facing):
 Let’s use the quadratic formula to solve some problems.
Learning targets (student facing):
 I can use the quadratic formula to solve an equation and interpret the solutions in terms of a situation.
Required materials:
 Scientific calculators
Standards:
 This lesson builds towards the standard: CCSS.HSAREI.B.4MS.AREI.4MO.A1.REI.A.2a
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