We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Express a Quadratic Function in Vertex Form

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Express A Quadratic Function In Vertex Form

Which of the following is the given quadratic equation in vertex form?

$y=5x^{2}+20x+27$

Possible Answers:

$y=5(x-4)^{2}+3$

$y=5(x+4)^{2}+7$

$y=5(x+2)^{2}+23$

$y=5(x+2)^{2}+27$

$y=5(x+2)^{2}+7$

Correct answer:

$y=5(x+2)^{2}+7$

Explanation:

To solve for the vertex form, we must start by completing the square:

y=5x^2+20x+27

$y+\; \; \; \; =5(x^2+4x+\; \; \; \; )+27$

y+5(4) =5(x^2+4x+4)+27

$y+20=5(x+2)^{2}+27$

$y=5(x+2)^{2}+7$

Report an Error

Example Question #1 : Express A Quadratic Function In Vertex Form

Which of the following is the appropriate vertex form of the following quadratic equation?

$y=3x^{2}+15x+32$

Possible Answers:

$y=3(x+5)^{2}+29$

$y=3(x+\frac{2}{5})^{2}+20$

$y=3(x+5)^{2}+17$

$y=3(x+\frac{5}{2})^{2}+\frac{103}{4}$

$y=3(x+\frac{5}{2})^{2}+\frac{53}{4}$

Correct answer:

$y=3(x+\frac{5}{2})^{2}+\frac{53}{4}$

Explanation:

This process outlines how to convert a quadratic function to vertex form:

$y=3x^{2}+15x+32$

$y+\; \; \; \; =3(x^{2}+5x+\; \; \; \; )+32$

$y+3(\frac{5}{2})^{2} =3(x^{2}+5x+(\frac{5}{2})^{2} )+32$

$y+\frac{75}{4} =3(x^{2}+5x+\frac{25}{4})+32$

$y=3(x^{2}+5x+\frac{25}{4})+32-\frac{75}{4}$

$y=3(x+\frac{5}{2})^{2}+\frac{128}{4}-\frac{75}{4}$

$y=3(x+\frac{5}{2})^{2}+\frac{53}{4}$

Report an Error

Example Question #2 : Express A Quadratic Function In Vertex Form

Give the coordinate pair of the vertex of this quadratic function x^2+2x-6 .

Possible Answers:

(h,k)=(1,7)

None of the other answers.

(h,k)=(-1,-7)

(h,k)=(1,-7)

(h,k)=(-1,7)

Correct answer:

(h,k)=(-1,-7)

Explanation:

Expressing quadratic functions in the vertex form is basically just changing the format of the equation to give us different information, namely the vertex. In order for us to change the function into this format we must have it in standard form ax^2+bx+c . After that, our goal is to change the function into the form y=a(x-h)^2+k . We do so as follows:

ax^2+bx+c=0

subtract the constant over to the other side ax^2+bx=-c

halve the b term, square it, and add to both sides. $ax^2+bx+\left(\frac{b}{2}\right)^2=-c+\left(\frac{b}{2}\right)^2$

Now factor the left side. $\left(x+\frac{b}{2}\right)^2=-c+\left(\frac{b}{2}\right)^2$

now simplify the right side and move that number back over to the left side and you will be left with a(x-h)^2+k . I recommend looking up an example with numbers before you begin or at least recognizing that the fractions will end up being whole numbers in most problems. Below is specific explanation of the problem at hand. Try to use the generic equation to find the answer before following the step by step approach below.

x^2+2x-6=0

move the constant over

x^2+2x=6

halve the b term and add to both sides

x^2+2x+1=6+1

factor the left side and simplify the right

(x+1)^2=7

move the constant over to achieve vertex form

(x+1)^2-7 is the final answer with vertex at (-1,-7). Note that the formula is y=a(x-h)^2+k .

try this shortcut after you have mastered the steps: (h,k)= (-b/2a, 4ac-b^2/4a) . Make sure you recognize that this formula gives you an x and y coordinate for the vertex and that each coordinate of the pair is fraction in the formula. This will give you the vertex of the equation if it is in standard form. However, don't rely on this as completing the square is also a method for finding the roots. So you need to know both methods before you cut the corner.

Report an Error

Example Question #1 : Express A Quadratic Function In Vertex Form

Express the following quadratic equation in vertex form.

y=2x^2-28x+108

Possible Answers:

y=2(x-7)^2+10

y=(x-5)^2+7

y=(x-14)^2+108

y=2(x-10)^2+7

Correct answer:

y=2(x-7)^2+10

Explanation:

To get the equation into vertex form, we factor the largest constant from the terms with a degree of greater than or equal to 1.

y=2x^2-28x+108

y=2(x^2-14x)+108

We then complete the square by following these steps

finding half of the coefficients of the term
squaring that result
and then adding that square to the expression for .

Keep in mind that what is done on one side of the equation must be done on the other.

y+2*7^2=2(x^2-14x+7^2)+108

y+98=2(x^2-14x+49)+108

And factoring the quadratic polynomial of x

y+98=2(x-7)^2+108

we get

y=2(x-7)^2+10

Report an Error

View Pre-Calculus Tutors

Zara
Certified Tutor

University of Manitoba, Bachelor in Arts, Mathematics.

View Pre-Calculus Tutors

James
Certified Tutor

University of Georgia, Bachelor in Arts, Political Science and Government.

View Pre-Calculus Tutors

Bhupinder
Certified Tutor

Panjab University, Bachelor of Engineering, Biotechnology. Hamburg University of Technology, Master of Science, Chemical Engi...

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in Phoenix, ACT Tutors in Philadelphia, ISEE Tutors in Dallas Fort Worth, English Tutors in Houston, GRE Tutors in San Francisco-Bay Area, SSAT Tutors in Denver, Algebra Tutors in Houston, Chemistry Tutors in San Francisco-Bay Area, GRE Tutors in Miami, Calculus Tutors in Los Angeles

Popular Courses & Classes

SSAT Courses & Classes in Miami, Spanish Courses & Classes in Los Angeles, ISEE Courses & Classes in Denver, LSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Boston, LSAT Courses & Classes in Denver, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Miami, SAT Courses & Classes in Chicago, SSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ACT Test Prep in Dallas Fort Worth, LSAT Test Prep in Chicago, ISEE Test Prep in Houston, GRE Test Prep in Atlanta, LSAT Test Prep in New York City, MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in San Diego, GRE Test Prep in Dallas Fort Worth, SSAT Test Prep in Atlanta, SAT Test Prep in Denver

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:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Precalculus : Express a Quadratic Function in Vertex Form

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Express A Quadratic Function In Vertex Form

Example Question #1 : Express A Quadratic Function In Vertex Form

Example Question #2 : Express A Quadratic Function In Vertex Form

Example Question #1 : Express A Quadratic Function In Vertex Form

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: