In this lesson, students practice rewriting factored quadratic expressions into standard form with non-zero leading coefficients. Then, students use some information to solve for \(m^2\) given information about \(k, k^2,\) and \(2km\). In the associated Algebra 1 lesson, students complete the square for quadratic expressions with a non-zero leading coefficient. Fluency in rewriting quadratic expressions in factored and standard forms supports students in the work of completing the square.
Part of the process for completing the square for quadratics with non-zero leading coefficient involves solving for \(k\) and \(m\) using information like that given in the second activity. By isolating that work here, students are supported to carry through the entire process in the associated Algebra 1 lesson.
Looking for and making use of structure (MP7) is essential when expanding a product of binomials into the standard form of a quadratic expression.
Lesson overview
- 14.1 Warm-up: Writing Quadratics in Standard Form (10 minutes)
- 14.2 Activity: Practice Writing Expressions in Standard Form (15 minutes)
- 14.3 Activity: Find the Values (15 minutes)
Learning goals:
- Compute the value of \(m^2\) given equations of the form \(k^2 = p\) and \(2km = q\).
- Practice methods for rewriting quadratic expressions of the form \((px+q)(rx+s)\) into standard form.
Learning goals (student facing):
- Let’s practice rewriting quadratic expressions.
Standards:
- This lesson builds towards the standard:CCSS.HSA-REI.B.4.aMS.A-REI.4aMO.A1.REI.A.2a
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