Quadratic Functions and Solutions

Lesson 8

Math

Unit 7

9th Grade

Lesson 8 of 13

Objective


Factor special cases of quadratic equations—difference of two squares.

Common Core Standards


Core Standards

  • A.SSE.A.1.A — Interpret parts of an expression, such as terms, factors, and coefficients.
  • A.SSE.A.2 — Use the structure of an expression to identify ways to rewrite it. For example, see x4 — y4 as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).
  • A.SSE.B.3.A — Factor a quadratic expression to reveal the zeros of the function it defines.

Criteria for Success


  1. Identify features of two linear binomials that when multiplied together result in a quadratic binomial difference of two squares. 
  2. Factor and solve quadratic equations that represent a difference of two squares.
  3. Describe graphical features of quadratic functions that are differences of two squares.

Tips for Teachers


Lessons 8 and 9 look at specific cases of factoring quadratic expressions—difference of two squares and perfect square trinomials. Depending on the needs of your students, these lessons can be kept separate or combined together. These lessons are also a good opportunity to spiral in other factoring problems from Lessons 4–7. 

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Anchor Problems


Problem 1

Aaron says that when you multiply two linear binomials, you will always get a trinomial. Alison disagrees and finds an example where two linear binomials multiplied together produce a quadratic binomial. 

Find an example that demonstrates Alison’s claim is true.

Guiding Questions

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Problem 2

Find the solutions to the quadratic equations below. 

a.  $${y=x^2-196}$$

b.  $${y=16x^2-121}$$

c.  $${y=75x^2-27 }$$

Guiding Questions

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Problem 3

Graphs of two quadratic functions are shown below. 

Which graph represents a quadratic function whose equation is a difference of two squares? Explain how you know.

Guiding Questions

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Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Factor each expression completely.

a.  $${x^2-36}$$

b.  $${12x^2-3}$$

c.  $${6x^2+34x-12}$$

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include spiraled problems that cover various factoring examples seen so far
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Lesson 7

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Lesson 9

Lesson Map

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Topic A: Features of Quadratic Functions

Topic B: Factoring and Solutions of Quadratic Equations

Topic C: Interpreting Solutions of Quadratic Functions in Context

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