In this lesson, students make connections between zeros of a function and solutions to associated equations. In particular, they recognize that the zeros they find from graphing technology do not always provide exact solutions. Next, students match expressions in the form \((ax+b)(cx+d)\) to their associated functions in standard form. In the associated Algebra 1 lesson, students examine quadratic expressions of the form \(ax^2 + bx + c\) for which \(a \neq 0\) and the factored form of the expressions. The work in this lesson supports students by giving them some additional background in the relationships between the 2 forms. Students must construct viable arguments and critique the reasoning of others (MP3) when they describe why they matched a factored expression to one in standard form. They also attend to precision (MP6) when they describe why their choice of option does not belong using mathematically accurate language.
Lesson overview
- 10.1 Warm-up: Which One Doesn’t Belong: Factored Quadratics (5 minutes)
- 10.2 Activity: Finding Solutions by Graphing (15 minutes)
- 10.3 Activity: Matching More Factored Expressions (20 minutes)
Learning goals:
- Recognize equations in expanded form and standard form are equivalent.
Learning goals (student facing):
- Let’s explore zeros on a graph.
Standards:
- This lesson builds towards the standards: CCSS.HSA-REI.DMS.A-REICCSS.HSA-SSE.B.3.aMS.A-SSE.3aMO.A1.SSE.A.3aMO.A1.REI.C
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