Quadratic Functions and Solutions

Lesson 9

Math

Unit 7

9th Grade

Lesson 9 of 13

Objective


Factor special cases of quadratic equations—perfect square trinomials.

Common Core Standards


Core Standards

  • 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 perfect square trinomial, where the first and last terms are perfect squares and the middle term is two times the product of the numbers that are squared (following the pattern $${a^2+2ab+b^2=(a+b)^2}$$). 
  2. Factor and solve quadratic equations that represent perfect square trinomials.
  3. Describe graphical features of quadratic functions that are perfect square trinomials.
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Anchor Problems


Problem 1

Expand each expression below as a product of two linear binomials and then multiply to write the product in standard form. 

a.  $${(x-5)^2}$$

b.  $${(x+4)^2}$$

c.  $${(x-3)^2}$$

d.  $${(2x+1)^2}$$

e.  $${(3x-2)^2}$$

Describe any patterns you notice between the square of the linear binomial and the resulting quadratic trinomial.

Guiding Questions

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Problem 2

Solve the quadratic equation and then sketch a graph of the parabola.

$${y=(x-4)^2}$$

Guiding Questions

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Problem 3

What is the value of $$c$$ in the equation below such that the quadratic equation is a perfect square trinomial?

$$y=x^2+12x+c$$

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


What binomial factor do the two expressions below have in common?

$${9x^2-6x+1}$$                        $${9x^2-1}$$

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 8

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Lesson 10

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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