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.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes


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

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

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

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

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

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

15-20 minutes


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

Target Task

5-10 minutes


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

Next

Solve quadratic equations by factoring. Compare solutions in different representations (graph, equation, and table).

Lesson 10
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Quadratic Functions

Topic B: Factoring and Solutions of Quadratic Equations

Topic C: Interpreting Solutions of Quadratic Functions in Context

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free