completing the square (continued) assignment quizlet

Study Guides > College Algebra

Completing the square.

• Given a quadratic equation that cannot be factored, and with [latex]a=1[/latex], first add or subtract the constant term to the right sign of the equal sign. [latex]{x}^{2}+4x=-1[/latex]
• Multiply the b term by [latex]\frac{1}{2}[/latex] and square it. [latex]\begin{array}{l}\frac{1}{2}\left(4\right)=2\hfill \\ {2}^{2}=4\hfill \end{array}[/latex]
• Add [latex]{\left(\frac{1}{2}b\right)}^{2}[/latex] to both sides of the equal sign and simplify the right side. We have [latex]\begin{array}{l}{x}^{2}+4x+4=-1+4\hfill \\ {x}^{2}+4x+4=3\hfill \end{array}[/latex]
• The left side of the equation can now be factored as a perfect square. [latex]\begin{array}{l}{x}^{2}+4x+4=3\hfill \\ {\left(x+2\right)}^{2}=3\hfill \end{array}[/latex]
• Use the square root property and solve. [latex]\begin{array}{l}\sqrt{{\left(x+2\right)}^{2}}=\pm \sqrt{3}\hfill \\ x+2=\pm \sqrt{3}\hfill \\ x=-2\pm \sqrt{3}\hfill \end{array}[/latex]
• The solutions are [latex]x=-2+\sqrt{3}[/latex], [latex]x=-2-\sqrt{3}[/latex].

Example 8: Solving a Quadratic by Completing the Square

Licenses & attributions, cc licensed content, specific attribution.

• College Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/ [email protected] :1/Preface. License: CC BY: Attribution .

Please add a message.

Message received. Thanks for the feedback.

You are using an outdated browser and it's not supported. Please upgrade your browser to improve your experience.

• LOGIN FOR PROGRAM PARTICIPANTS
• PROGRAM SUPPORT

Completing the Square (Continued)

Description.

Students rewrite quadratic expressions given in standard form, ax^2+bx+c (with a≠1), as equivalent expressions in completed-square form, a(x-h)^2+k.

There may be cases when our downloadable resources contain hyperlinks to other websites. These hyperlinks lead to websites published or operated by third parties. UnboundEd and EngageNY are not responsible for the content, availability, or privacy policies of these websites.

• Algebra I Module 4, Topic B, Lesson 12: Student Version
• Algebra I Module 4, Topic B, Lesson 12: Teacher Version

Related Guides and Multimedia

Our professional learning resources include teaching guides, videos, and podcasts that build educators' knowledge of content related to the standards and their application in the classroom.

There are no related guides or videos. To see all our guides, please visit the Enhance Instruction section here .

• Show all results for " "

Completing the Square

Study Flashcards

10 Questions

Which technique can be used to rewrite a quadratic expression as a perfect square trinomial.

Completing the square

Which step is involved in solving quadratic equations by completing the square?

Factoring the perfect square trinomial

What is the term needed to complete the square if the quadratic expression is x^2 + 6x?

When completing the square, what is the square of half the coefficient of the linear x.

The quadratic term

What property is used to solve the resulting equation after completing the square?

The square root property

What is the term needed to complete the square if the quadratic expression is $x^2 + 6x$?

Add the term needed to complete the square

Square root property

When completing the square, what is the square of half the coefficient of the linear term?

The constant term

Study Notes

• To rewrite a quadratic expression as a perfect square trinomial, the technique of completing the square is used.

Solving Quadratic Equations

• To solve quadratic equations by completing the square, the step involved is adding a value to both sides of the equation to make one side a perfect square trinomial.

Completing the Square Formula

• To complete the square, the term needed is $(b/2)^2$, where $b$ is the coefficient of the linear term $x$.
• For the quadratic expression $x^2 + 6x$, the term needed to complete the square is $(6/2)^2 = 3^2 = 9$.

Solving the Resulting Equation

• After completing the square, the property used to solve the resulting equation is the difference of squares property, which states that $a^2 - b^2 = (a + b)(a - b)$.

Test your knowledge on solving quadratic equations by completing the square with this interactive quiz. Learn how to rewrite quadratic equations and find their solutions using the completing the square method.

Make Your Own Quizzes and Flashcards

Convert your notes into interactive study material.

More Quizzes Like This

Completing the Square Method

Solving Quadratic Equations and Identifying Pure Quadratic Equations Q...

Completing the Square - Intermediate Math Problems

Completing the Square Practice Problems

Upgrade to continue

Today's Special Offer

Save an additional 20% with coupon: SAVE20

Upgrade to a paid plan to continue

Trusted by students, educators, and businesses worldwide.

We are constantly improving Quizgecko and would love to hear your feedback. You can also submit feature requests here: feature requests.

Create your free account

By continuing, you agree to Quizgecko's Terms of Service and Privacy Policy .

live the #mathlife with lessons, activities, videos, & much more

Completing the square resources, completing the square foldable for interactive math notebooks.

Create perfect square trinomials to solve quadratic equations!

Completing the Square Task Cards

Students can get plenty of practice with these 2 sets of task cards for completing the square!

YouTube Video: Completing the Square

Quizlet study set: completing the square.

Flow along as I guide you through my notes on completing the square!

Practice by using flash cards or play a game of Quizlet Live!

iteachalgebra

New Jersey, USA

[email protected]

Copyright © 2018 iteachalgebra - All Rights Reserved.

Powered by GoDaddy

HIGH SCHOOL

• ACT Tutoring
• SAT Tutoring
• PSAT Tutoring
• ASPIRE Tutoring
• SHSAT Tutoring
• STAAR Tutoring

GRADUATE SCHOOL

• MCAT Tutoring
• GRE Tutoring
• LSAT Tutoring
• GMAT Tutoring
• AIMS Tutoring
• HSPT Tutoring
• ISAT Tutoring
• SSAT Tutoring

Search 50+ Tests

Loading Page

math tutoring

• Elementary Math
• Pre-Calculus
• Trigonometry

science tutoring

Foreign languages.

• Mandarin Chinese

elementary tutoring

• Computer Science

Search 350+ Subjects

• Video Overview
• Tutor Selection Process
• Online Tutoring
• Mobile Tutoring
• Instant Tutoring
• How We Operate
• Our Guarantee
• Impact of Tutoring
• Reviews & Testimonials
• About Varsity Tutors

Algebra II : Completing the Square

Study concepts, example questions & explanations for algebra ii, all algebra ii resources, example questions, example question #1 : completing the square.

Complete the square in order to find the vertex of this parabola.

To find the vertex of the parabola, you have to get it into vertex form:

To get to vertex form, we have to complete the square.

Move the 7 over to the other side by subtracting 7 from both sides of the equation:

You're going to have to add something to both sides of the equation...

...the question now is what . What number, when put in the box, would create a "perfect square" on the right-hand side of the equation?

Well, a perfect square trinomial is one whose factors are the same, like so:

Now we can factor the right-hand side very neatly:

After we clean up a bit...

Solve by completing the square:

To complete the square, the equation must be in the form:

Solve the following equation by completing the square. Use a calculator to determine the answer to the closest hundredth.

No solution

To solve by completing the square, you should first take the numerical coefficient to the “right side” of the equation:

Then, divide the middle coefficient by 2:

Square that and add it to both sides:

Now, you can factor the quadratic:

Take the square root of both sides:

Finish out the solution:

Example Question #4 : Completing The Square

Now, you can easily factor the quadratic:

Example Question #5 : Completing The Square

Example Question #6 : Completing The Square

Example Question #7 : Completing The Square

Example Question #8 : Completing The Square

Example Question #9 : Completing The Square

To make completing the square sensible, we divide both sides by 2.

We now divide the x coefficient by 2, square the result, and add that to both sides.

Since the right side is now a perfect square, we can rewrite it as a square binomial.

Take the square root of both sides, simplify the radical and solve for x.

Example Question #10 : Completing The Square

We start by moving the constant term of the quadratic to the other side of the equation, to set up the "completing the square" format.

Now to make completing the square sensible, we divide boths sides by 2 so that x^2 will not have a coefficient. 

Now we can complete the square by dividing the x coefficient by 2 and squaring the result, then adding that result to both sides.

Because the left side is now a perfect square, we can rewrite it as a squared binomial.

Take the square root of both sides, and then solve for x.

Report an issue with this question

If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105

Or fill out the form below:

Contact Information

Complaint details.

Pardon Our Interruption

As you were browsing something about your browser made us think you were a bot. There are a few reasons this might happen:

• You've disabled JavaScript in your web browser.
• You're a power user moving through this website with super-human speed.
• You've disabled cookies in your web browser.
• A third-party browser plugin, such as Ghostery or NoScript, is preventing JavaScript from running. Additional information is available in this support article .

To regain access, please make sure that cookies and JavaScript are enabled before reloading the page.

Have an account?

Completing the Square

Mathematics.

16 questions

Introducing new   Paper mode

No student devices needed.   Know more

• 1. Multiple Choice Edit 1.5 minutes 1 pt What do you do to the b value to correctly complete the square? square it divide it by 2 and square the result divide it by 2 and take the square root of the result divide it by 2 only
• 2. Multiple Choice Edit 30 seconds 1 pt To solve by completing the square, what needs to be moved in this equation? x 2 = 9 - 4x the -4x the 9 the x 2
• 3. Multiple Choice Edit 30 seconds 1 pt What is the first step to solving THIS equation by completing the square? a 2 + 10a + 21 = 0 Set the equation equal to zero Divide 10 by 2 and add the result to both sides Add a 2 and 10a together Subtract the 21
• 4. Multiple Choice Edit 1.5 minutes 1 pt When factoring x 2  - 4x + 4 = 20, what goes in the blank? (x - __ ) 2 = 20 4 2 8 20
• 5. Multiple Choice Edit 30 seconds 1 pt What is one of the solutions to this equation? (2x - 1) 2 = 49 7 -7 -4 -3
• 6. Multiple Choice Edit 1.5 minutes 1 pt Complete the Square x 2  + 6x = 5 (x + 3) 2  = 5 (x + 6) 2  = 9 (x + 3) 2  = 14 (x + 6) 2  = 14
• 7. Multiple Choice Edit 1.5 minutes 1 pt Solve the equation by completing the square and then finding the roots.  x 2 + 6x - 4 = 36 x = -7, 7 x = 4, -10 x = -4 +- √7 x = 10, -4
• 8. Multiple Choice Edit 1 minute 1 pt Solve by completing the square. x 2 +12x = 5 X = 6 + √41 or  6 − √41 X= 35 or 47 X = −6 + √41 or  −6 − √41 X = √35 or √47
• 9. Multiple Choice Edit 30 seconds 1 pt Solve the following equation by completing the square: n 2 - 2n - 3 = 0 {3 and-1} {4 and -4} {5 and -3} {8 and -7}
• 10. Multiple Choice Edit 30 seconds 1 pt Solve the following equation by completing the square: n 2 = 18n + 40 {11 and -11} {16 and 2} {20 and -2} {10 and -4}
• 11. Multiple Choice Edit 30 seconds 1 pt Solve by completing the square: k 2 − 12k + 23 = 0 {6 + √13, 6 - √13} {-6 + √13, -6 - √13} {6 + √59, 6 - √59} {-6 + √59, -6 - √59}
• 12. Multiple Choice Edit 1.5 minutes 1 pt Complete the square for x 2 + 12x + ____ x 2 + 12x + 144 x 2 + 12x + 36 x 2 + 12x - 36 x 2 + +12x - 144
• 13. Multiple Choice Edit 30 seconds 1 pt Complete the square. x 2  + 6x + ____ x 2  + 6x + 9 x 2  + 6x - 36 x 2  + 6x + 36 x 2  + 6x - 9
• 14. Multiple Choice Edit 30 seconds 1 pt Complete the Square x 2 + 10x + ____ x 2 + 10x - 100 x 2 + 10x + 100 x 2 + 10x - 25 x 2 + 10x + 25
• 15. Multiple Choice Edit 3 minutes 1 pt Solve by completing the square. Round. x 2  -4x = 5 11 and -7 1 and 3 1.73 and -1.73 5 and -1
• 16. Multiple Choice Edit 30 seconds 1 pt Solve by completing the square. y 2 + 10y = -9 1 and -12 -1 and -9 1 and -9 1 and -1

Explore all questions with a free account

Continue with email

Continue with phone