We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Algebra II

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 #83 : Intermediate Single Variable Algebra

Solve the following equation using the quadratic form:

$x^{\frac{2}{3}}-9x^{\frac{1}{3}}+20=0$

Possible Answers:

x=124, 65

x=125, 64

x=120, 64

x=125, 65

x=124, 64

Correct answer:

x=125, 64

Explanation:

Factor and solve:

$x^{\frac{2}{3}}-9x^{\frac{1}{3}}+20=0$

$(x^{\frac{1}{3}})^2-9x^{\frac{1}{3}}+20=0$

$(x^\frac{1}{3}-5)(x^\frac{1}{3}-4)=0$

$x^\frac{1}{3}=5$

x=125

$x^\frac{1}{3}=4$

x=64

Therefore the equation has two solutions.

Report an Error

Example Question #84 : Intermediate Single Variable Algebra

Solve the following equation using the quadratic form:

n^6+9n^3+8=0

Possible Answers:

$n=-3,-1,1 \pm i\sqrt{3}, \frac{1 \pm i\sqrt{3}}{2}$

$n=-3,-2,1 \pm i\sqrt{3}, \frac{1 \pm i\sqrt{3}}{2}$

$n=-3,-2,2 \pm i\sqrt{3}, \frac{1 \pm i\sqrt{3}}{2}$

$n=-2,-1,1 \pm i\sqrt{3}, \frac{1 \pm i\sqrt{3}}{2}$

$n=-3,-1,1 \pm i\sqrt{3}, \frac{3 \pm i\sqrt{3}}{2}$

Correct answer:

$n=-2,-1,1 \pm i\sqrt{3}, \frac{1 \pm i\sqrt{3}}{2}$

Explanation:

Factor and solve:

n^6+9n^3+8=0

(n^3)^2+9n^3+8=0

(n^3+8)(n^3+1)=0

(n+2)(n^2-2n+4)(n+1)(n^2-n+1)=0

Each of these factors gives solutions to the equation:

n=-2

n=-1

$n=1 \pm i\sqrt{3}$

$n=\frac{1 \pm i\sqrt{3}}{2}$

Report an Error

Example Question #22 : Finding Roots

The product of two consecutive positive numbers is 156 . What is the sum of the two numbers?

Possible Answers:

Correct answer:

Explanation:

Let the first number and x+1= the second number.

The equation to sovle becomes x(x+1)=156 , or $x^{2}+x-156=0$ .

Factoring we get (x+13)(x-12)=0 , so the solution is $x=-13 \; \; or\; \; x=12$ . The problem states that the numbers are positive, so the correct numbers are and , which sum to .

Report an Error

Example Question #332 : Algebra Ii

Two positive, consecutive odd numbers have a product of 143 . What is their sum?

Possible Answers:

Correct answer:

Explanation:

Let first odd number and x+2= second odd number. Then:

x(x+2)=143

Use the distributive property and subtract 143 from both sides to get $x^{2}+2x-143=0$ .

Factoring we get (x+13)(x-11)=0 .

Solving we get $x+13=0\; or\; x-11=0$ , so $x=-13\; or\; x=11$ .

The problem stated that the numbers were positive so the answer becomes 11+13=24 .

Report an Error

Example Question #333 : Algebra Ii

Find the sum of the solutions to:

$\frac{-6}{x^2} + \frac{1}{x} + 1 = 0$

Possible Answers:

Correct answer:

Explanation:

Multiply both sides of the equation by x^2 , to get

-6 + x + x^2 = 0

This can be factored into the form

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

So we must solve

x+3 = 0

and

x-2 = 0

to get the solutions.

The solutions are:

x =-3, 2

and their sum is .

Report an Error

Example Question #1 : Completing The Square

$f(x)=x^{2}-4x+7$

Find the vertex of the parabola by completing the square.

Possible Answers:

$\small (7,0)$

$\small (1,4)$

$\small (2,3)$

$\small (3,2)$

$\small (0,7)$

Correct answer:

$\small (2,3)$

Explanation:

To find the vertex of a parabola, we must put the equation into the vertex form:

$\small f(x)=a[b(x-h)]^{2}+k$

The vertex can then be found with the coordinates (h, k).

To put the parabola's equation into vertex form, you have to complete the square. Completing the square just means adding the same number to both sides of the equation -- which, remember, doesn't change the value of the equation -- in order to create a perfect square.

Start with the original equation:

$f(x)=x^{2}-4x+7$

Put all of the terms on one side:

$f(x)-7=x^{2}-4x$

Now we know that we have to add something to both sides in order to create a perfect square:

$f(x)+7+\square =x^{2}-4x+\square$

In this case, we need to add 4 on both sides so that the right-hand side of the equation factors neatly.

$f(x)-7+4=x^{2}-4x+4$

Now we factor:

$f(x)-3=(x-2)^{2}$

Once we isolate f(x) , we have the equation in vertex form:

$f(x)=(x-2)^{2}+3$

Thus, the parabola's vertex can be found at $\small (2,3)$ .

Report an Error

Example Question #2 : Completing The Square

Complete the square:

2x^2+3x+2=0

Possible Answers:

$x=\frac{-2 \pm i\sqrt{7}}{3}$

$x=\frac{-3 \pm i\sqrt{7}}{4}$

$x=\frac{-2 \pm i\sqrt{7}}{4}$

$x=\frac{-1 \pm i\sqrt{7}}{4}$

$x=\frac{-3 \pm i\sqrt{7}}{3}$

Correct answer:

$x=\frac{-3 \pm i\sqrt{7}}{4}$

Explanation:

Begin by dividing the equation by and subtracting from each side:

2x^2+3x+2=0

$x^2+\frac{3}{2}x = -1$

Square the value in front of the and add to each side:

$x^2+\frac{3}{2}x +\frac{9}{16} = -1+\frac{9}{16}$

Factor the left side of the equation:

$(x+\frac{3}{4})^2 = \frac{-7}{16}$

Take the square root of both sides and simplify:

$x+\frac{3}{4} = \frac{\pm \sqrt{-7}}{4}$

$x = \frac{-3 \pm i\sqrt{7}}{4}$

Report an Error

Example Question #3 : Completing The Square

Use factoring to solve the quadratic equation:

6x^2+7x-3=0

Possible Answers:

$x=-\frac{3}{2},\frac{2}{3}$

$x=-\frac{3}{2},\frac{1}{4}$

$x=-\frac{3}{4},\frac{1}{3}$

$x=-\frac{3}{2},\frac{1}{3}$

$x=-\frac{3}{4},\frac{1}{4}$

Correct answer:

$x=-\frac{3}{2},\frac{1}{3}$

Explanation:

Factor and solve:

6x^2+7x-3=0

6x^2 +9x-2x-3=0

Factor like terms:

3x(2x+3)-1(2x+3)=0

Combine like terms:

(2x+3)(3x-1)=0

$x=-\frac{3}{2},\frac{1}{3}$

Report an Error

Example Question #51 : Quadratic Equations And Inequalities

Complete the square:

2n^2+n-21=0

Possible Answers:

$n=-\frac{7}{2},2$

$n=-\frac{5}{2},3$

$n=-\frac{7}{2},4$

$n=-\frac{7}{2},3$

$n=-\frac{9}{2},3$

Correct answer:

$n=-\frac{7}{2},3$

Explanation:

Begin by dividing the equation by and adding 10.5 to each side:

2n^2+n-21=0

$n^2+\frac{1}{2}n = \frac{21}{2}$

Square the value in front of the and add to each side:

$n^2+\frac{1}{2}n + \frac{1}{16} = \frac{21}{2} + \frac{1}{16}$

Factor the left side of the equation:

$(n+\frac{1}{4})^2 = \frac{169}{16}$

Take the square root of both sides and simplify:

$n+\frac{1}{4} = \frac{\pm 13}{4}$

$n = \frac{-1 \pm 13}{4}$

$n=-\frac{7}{2},3$

Report an Error

Example Question #5 : Completing The Square

Complete the square:

3x^2+4x+2=0

Possible Answers:

$x=\frac{-4 \pm i\sqrt{2}}{3}$

$x=\frac{-3 \pm i\sqrt{2}}{3}$

$x=\frac{-2 \pm i\sqrt{3}}{3}$

$x=\frac{-2 \pm i\sqrt{2}}{3}$

$x=\frac{-2 \pm i\sqrt{2}}{4}$

Correct answer:

$x=\frac{-2 \pm i\sqrt{2}}{3}$

Explanation:

Begin by dividing the equation by and subtracting $\frac{2}{3}$ from each side:

3x^2+4x+2=0

$x^2+\frac{4}{3}x = -\frac{2}{3}$

Square the value in front of the and add to each side:

$x^2+\frac{4}{3}x +\frac{4}{9} = -\frac{2}{3}+\frac{4}{9}$

Factor the left side of the equation:

$(x+\frac{2}{3})^2 = \frac{-2}{9}$

Take the square root of both sides and simplify:

$x+\frac{2}{3} = \frac{\pm \sqrt{-2}}{3}$

$x = \frac{-2 \pm i\sqrt{2}}{3}$

Report an Error

View Tutors

Justin
Certified Tutor

dongguk uni, Bachelor, international commerce. south eastern uni, Master's/Graduate, management information system.

View Tutors

Theodore
Certified Tutor

Harvard University, Bachelor in Arts, Folklore Studies. HoHoKus-Hackensack School of Business and Medical Sciences, Doctor of...

View Tutors

Stephanie
Certified Tutor

University of North Carolina at Charlotte, Bachelor in Arts, International Business.

All High School Math Resources

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

Popular Subjects

Spanish Tutors in Philadelphia, GMAT Tutors in New York City, Reading Tutors in Atlanta, English Tutors in Miami, Computer Science Tutors in San Diego, SAT Tutors in Washington DC, SAT Tutors in New York City, Chemistry Tutors in Dallas Fort Worth, GRE Tutors in Boston, Physics Tutors in Washington DC

Popular Courses & Classes

GMAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Phoenix, ACT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Seattle, GMAT Courses & Classes in San Diego, SSAT Courses & Classes in Chicago, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Philadelphia

Popular Test Prep

ACT Test Prep in Dallas Fort Worth, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in New York City, GMAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Los Angeles, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Seattle, LSAT Test Prep in Boston, SSAT Test Prep in New York City, ISEE Test Prep in Chicago

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 : Algebra II

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #83 : Intermediate Single Variable Algebra

Example Question #84 : Intermediate Single Variable Algebra

Example Question #22 : Finding Roots

Example Question #332 : Algebra Ii

Example Question #333 : Algebra Ii

Example Question #1 : Completing The Square

Example Question #2 : Completing The Square

Example Question #3 : Completing The Square

Example Question #51 : Quadratic Equations And Inequalities

Example Question #5 : Completing The Square

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: