The purpose of this lesson is for students to solve systems of equations involving quadratics. Unlike systems of linear equations, systems involving quadratic functions can have 0, 1, or 2 distinct solutions, in addition to the infinitely many solutions case. Students begin the lesson by focusing on structure to identify possible solutions to a series of systems of equations (MP7). Building on this, students then combine their skills solving systems of equations using substitution and solving quadratic equations to identify all solutions to systems of equations involving at least one quadratic function.
The last activity is meant to make clear that while algebraic solving methods are useful, technology helps us identify solutions to systems of equations in which the steps needed to solve by hand are less obvious. This activity also asks students to consider what a possible factor of a polynomial expression written in standard form could be, which will be the focus of the following lessons leading into the Remainder Theorem.
Lesson overview
 11.1 Warmup: Math Talk: When \(f\) Meets \(g\) (5 minutes)

11.2 Activity: More Points of Intersection (20 minutes)
 Includes "Are you Ready for More?" extension problem
 11.3 Activity: Graphing to Find Points of Intersection (10 minutes)
 Lesson Synthesis
 11.4 Cooldown: Find Some More Points (5 minutes)
Learning goals:
 Calculate the solution to a system of polynomial equations.
Learning goals (student facing):
 Let’s think about two polynomials at once.
Learning targets (student facing):
 I can find where two polynomial functions intersect.
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 standards: CCSS.HSAAPR.B.3MS.AAPR.3CCSS.HSAREI.B.4MS.AREI.4CCSS.HSAREI.C.7MS.AREI.7MO.A2.APR.A.5MO.A1.REI.A.2cMO.A1.REI.B.4
 This lesson builds towards the standard: CCSS.HSAAPR.BMO.A2.APR.A
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