Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

x^4-9=0

Possible Answers:

$x=\pm\sqrt{2}, \pm i\sqrt{2}$

$x=\pm\sqrt{5}, \pm i\sqrt{5}$

$x=\pm\sqrt{6}, \pm i\sqrt{6}$

$x=\pm\sqrt{4}, \pm i\sqrt{4}$

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

Correct answer:

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

Explanation:

Factor the equation and solve:

x^4-9=0

(x^2-3)(x^2+3)=0

x^2 = 3

$x = \pm \sqrt{3}$

x^2 = -3

$x = \pm i\sqrt{3}$

Therefore there are four answers:

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

Report an Error

Example Question #1 : Simplifying And Expanding Quadratic Equations

Solve the following equation using the quadratic form:

$x-4\sqrt{x}-45=0$

Possible Answers:

x=36

x=49

x=64

x=81

x=25

Correct answer:

x=81

Explanation:

Factor the equation and solve:

$x-4\sqrt{x}-45=0$

$(\sqrt{x}-9)(\sqrt{x}+5)=0$

$\sqrt{x}=9$

x=81

$\sqrt{x}=-5$

This has no solutions.

Therefore there is only one answer:

x=81

Report an Error

Example Question #1 : Understanding Quadratic Equations

Evaluate $(2x+2y)^{2}$

Possible Answers:

$4x^{2}+8xy+4y^{2}$

$\dpi{100} 4x^{2}+4xy+4y^{2}$

$\dpi{100} 2x^{2}+4xy+2y^{2}$

$\dpi{100} 4x^{2}+4y^{2}$

$\dpi{100} x^{2}+xy+y^{2}$

Correct answer:

$4x^{2}+8xy+4y^{2}$

Explanation:

In order to evaluate $\dpi{100} (2x+2y)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

$\dpi{100} \dpi{100} (2x+2y)^{2}=(2x+2y)(2x+2y)$

Multiply terms by way of FOIL method.

=(2x*2x)+(2x*2y)+(2y*2x)+(2y*2y)

Now multiply and simplify.

$=4x^{2}+4xy+4xy+4y^{2}$

$\rightarrow 4x^{2}+8xy+4y^{2}$

Report an Error

Example Question #2 : Understanding Quadratic Equations

Evaluate $(x-2)^{2}$

Possible Answers:

$\dpi{100} 4x^{2}-4x+4$

$\dpi{100} x^{2}-4$

$\dpi{100} x^{2}-2x+4$

$x^{2}-4x+4$

$\dpi{100} x^{2}+4$

Correct answer:

$x^{2}-4x+4$

Explanation:

In order to evaluate $\dpi{100} \dpi{100} (x-2)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

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

Multiply terms by way of FOIL method.

=(x*x)+(x*-2)+(-2*x)+(-2*-2)

Now multiply and simplify, paying attention to signs.

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

$\rightarrow x^{2}-4x+4$

Report an Error

Example Question #3 : Understanding Quadratic Equations

Evaluate (x+2y)*(2x-y)

Possible Answers:

$\dpi{100} x^{2}+2xy-y^{2}$

$\dpi{100} -2x^{2}-3xy+2y^{2}$

$\dpi{100} 4x^{2}+xy-4y^{2}$

$2x^{2}+3xy-2y^{2}$

$\dpi{100} 2x^{2}+4xy-2y^{2}$

Correct answer:

$2x^{2}+3xy-2y^{2}$

Explanation:

In order to evaluate (x+2y)*(2x-y) one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

Multiply terms by way of FOIL method.

=(x*2x)+(x*-y)+(2y*2x)+(2y*-y)

Now multiply and simplify, paying attention to signs.

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

$\rightarrow 2x^{2}+3xy-2y^{2}$

Report an Error

Example Question #4 : Understanding Quadratic Equations

Evaluate $(x-y)^{2}$

Possible Answers:

$x^{2}-2xy+y^{2}$

$\dpi{100} 2x^{2}-4xy+2y^{2}$

$x^{2}+y^{2}$

$\dpi{100} x^{2}-y^{2}$

$\dpi{100} -x^{2}+2xy-y^{2}$

Correct answer:

$x^{2}-2xy+y^{2}$

Explanation:

In order to evaluate $\dpi{100} \dpi{100} (x-y)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

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

Multiply terms by way of FOIL method.

=(x*x)+(x*-y)+(-y*x)+(-y*-y)

Now multiply and simplify, paying attention to signs.

$=x^{2}+(-xy)+(-xy)+(y^{2})$

$\rightarrow x^{2}-2xy+y^{2}$

Report an Error

Example Question #1 : Understanding Quadratic Equations

FOIL (x+2)(x-2) .

Possible Answers:

x^2+4x+4

x^2-2x+2

x^2+4

x^2+x-2

x^2-4

Correct answer:

x^2-4

Explanation:

Remember FOIL stands for First Outer Inner Last. That means we can take (x+2)(x-2) and turn it into x^2+2x-2x-4 .

Simplify to get x^2-4 .

Report an Error

Example Question #42 : Intermediate Single Variable Algebra

FOIL (x+5)^2 .

Possible Answers:

x^2+25

x^2+25x+25

x^2-10x+25

x^2+10x+25

5x^2

Correct answer:

x^2+10x+25

Explanation:

(x+5)^2 is the same thing as (x+5)(x+5) .

Remember that FOIL stands for First Outer Inner Last.

For this problem, that would be x^2+5x+5x+25 .

Simplify that to x^2+10x+25 .

Report an Error

Example Question #43 : Intermediate Single Variable Algebra

FOIL (x+5)(x-1) .

Possible Answers:

x^2+24

x^2-4x-5

x^2+5x+5

x^2+4x-5

x^2-5

Correct answer:

x^2+4x-5

Explanation:

Remember that FOIL stands for First Outer Inner Last.

For this problem that would give us:

(x+5)(x-1)

x^2-x+5x-5

Simplify.

x^2+4x-5

Report an Error

Example Question #44 : Intermediate Single Variable Algebra

FOIL (x+2)(x-2) .

Possible Answers:

x^2-4x

x^2+4

-x^2+4

x^2-4

x^2-4x-4

Correct answer:

x^2-4

Explanation:

Remember that FOIL stands for First Outer Inner Last.

For this problem that would give us:

(x+2)(x-2)

=x^2-2x+2x-4

Simplify:

=x^2-4

Report an Error

View Tutors

Anne
Certified Tutor

University of Maryland-Baltimore, Doctor of Science, Accounting.

View Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Tutors

Tonja
Certified Tutor

McNeese State University, Bachelor in Arts, English.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Miami, LSAT Tutors in New York City, SAT Tutors in Seattle, Physics Tutors in San Francisco-Bay Area, Physics Tutors in Phoenix, LSAT Tutors in Los Angeles, Calculus Tutors in San Francisco-Bay Area, French Tutors in Atlanta, ISEE Tutors in Chicago, SSAT Tutors in Miami

Popular Courses & Classes

MCAT Courses & Classes in New York City, SAT Courses & Classes in Washington DC, SAT Courses & Classes in Atlanta, ACT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, ACT Courses & Classes in New York City, SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in New York City, ISEE Courses & Classes in San Diego

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in New York City, GRE Test Prep in Philadelphia, SSAT Test Prep in Washington DC, SSAT Test Prep in Chicago, SAT Test Prep in Washington DC, GRE Test Prep in Los Angeles, SSAT Test Prep in New York City, GMAT Test Prep in Los Angeles, SSAT Test Prep in Boston

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

High School Math : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Quadratic Equations And Inequalities

Example Question #1 : Simplifying And Expanding Quadratic Equations

Example Question #1 : Understanding Quadratic Equations

Example Question #2 : Understanding Quadratic Equations

Example Question #3 : Understanding Quadratic Equations

Example Question #4 : Understanding Quadratic Equations

Example Question #1 : Understanding Quadratic Equations

Example Question #42 : Intermediate Single Variable Algebra

Example Question #43 : Intermediate Single Variable Algebra

Example Question #44 : Intermediate Single Variable Algebra

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: