Quadratic Equations and Applications

Lesson 2

Math

Unit 8

9th Grade

Lesson 2 of 15

Objective


Complete the square.

Common Core Standards


Core Standards

  • A.SSE.B.3.B — Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Foundational Standards

  • A.SSE.A.2
  • A.SSE.B.3.A

Criteria for Success


  1. Create a perfect square trinomial within a quadratic expression.
  2. Understand the process for completing the square when the leading coefficient is equal to $$1$$, when the leading coefficient is not equal to $$1$$, when the value of $$b$$ is even, and when the value of $$b$$ is odd.
  3. Understand how to maintain the equivalence between expressions or the balance within an equation.

Tips for Teachers


  • In terms of pacing, this lesson may be extended over 2 days to adequately cover all of the different variations of expressions and equations. Students will have time to practice and apply this skill of completing the square in Lessons 3–5. 
  • The approach taken in this lesson focuses on an algebraic method versus a geometric method. If you would like to take a geometric approach, the Desmos activity Introducton to Completing the Square is a great resource.
  • This lesson focuses on the process of completing the square. In Lesson 3, students will apply this process to find the vertex and to solve for the roots. 
Fishtank Plus

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

Anchor Problems

25-30 minutes


Problem 1

Complete the table with the missing values in order to "complete the square."

$${x^2+6x+9}$$ $${{{(x+}}3{{{)^2}}}}$$
$${x^2+8x+16}$$  
$${x^2-10x+25}$$  
  $${{(x-}7{{{)^2}}}}$$
$${x^2-20x+}$$_______ $${(x-}$$_______$${{{)^2}}}$$
$${x^2+16x+}$$______ $${{(x+}}$$_______$${{{)^2}}}$$
$${x^2+bx+}$$______ $${{(x+}}$$_______$${{{)^2}}}$$

 

Guiding Questions

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

References

f(t) Completing the Square

Completing the Square by Kate Nowak is made available on Function of Time under the CC BY-NC-SA 3.0 license. Accessed July 12, 2018, 4:32 p.m..

Problem 2

Complete the square in each expression below to include a perfect square binomial.

a.   $${x^2+6x+11}$$

b.    $${x^2+5x-10}$$

Guiding Questions

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

Problem 3

Rewrite each equation into vertex form by completing the square.

a.   $${x^2-12x+5=y}$$

b.   $${2x^2+16x+3=y}$$

Guiding Questions

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

References

EngageNY Mathematics Algebra I > Module 4 > Topic B > Lesson 12Example 1

Algebra I > Module 4 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

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


  1. What is the minimum value taken by the expression $${{{(x-}}4)^2+6}$$? How does the structure of the expression help to see why?
  2. Rewrite the quadratic expression $${ x^2-6x-3}$$ in the form $${{(x-}}$$ _____$${{ )^2+}}$$ ______ .
  3. Rewrite the quadratic expression $${-2x^2+4x+3}$$ in the form  ____ $${{(x-}}$$ _____$${{ )^2+}}$$ ______ .

References

Illustrative Mathematics Rewriting a Quadratic Expression

Rewriting a Quadratic Expression, accessed on July 12, 2018, 11:55 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

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.

Next

Complete the square to identify the vertex and solve for the roots of a quadratic function.

Lesson 3
icon/arrow/right/large

Lesson Map

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

Topic A: Deriving the Quadratic Formula

Topic B: Transformations and Applications

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