Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #34 : Finding Roots

Find the roots of the given quadratic.

x^2+10x-24

Possible Answers:

(x+12)(x-2)

(x-12)(x+2)

(x+14)(x-2)

(x-12)(x-2)

(x+12)(x+2)

Correct answer:

(x+12)(x-2)

Explanation:

The roots of a quadratic can be found by factoring. Factoring the solution will give you an expression that when multiplying will result in the initial quadratic.

The roots for this expression are (x+12)(x-2) . Similarly the roots of a quadratic can be found using the quadratic quadratic formula where the parent function of a quadratic is represented as ax^2+bx+c and the quadratic formula is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ .

Report an Error

Example Question #33 : Solving Quadratic Equations

What are the roots of the following graph?

Graph for questions

Possible Answers:

x=-1

x=5

y=9

None of the above

y=-1

y=5

x=2

Correct answer:

x=-1

x=5

Explanation:

Roots when looking at a graph are simply the x-values of where the function crosses the x-axis.

Which, when looking at this graph, it is clearly

x=-1 and x=5

Report an Error

Example Question #34 : Solving Quadratic Equations

Solve the equation.

3d^2+81=0

Possible Answers:

$d=\pm\3$

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

$d=\pm\sqrt{3}$

$d=\pm\3i$

Correct answer:

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

Explanation:

To solve this equation perform the oppisite operation to isolate the variable.

3d^2+81=0

3d^2=-81

d^2=-27

$d=\pm \sqrt{-27}$

Recall that the square root of a negative number results in an imaginary number.

i^2=-1

Therefore,

$d=\pm i \sqrt{27}$

$d=\pm\3i \sqrt{3}$ .

Report an Error

Example Question #33 : Finding Roots

Solve the equation.

6x^2=-126

Possible Answers:

$x=\pm{i\sqrt{21}}$

$x=\pm{\sqrt{21}}$

$x=\pm{\sqrt{-21}}$

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

Correct answer:

$x=\pm{i\sqrt{21}}$

Explanation:

To solve this equation perform the oppisite operation to isolate the variable.

6x^2=-126

x^2=-21

Recall that the square root of a negative number is an imaginary number.

i^2=-1

Therefore,

$x=\pm{\sqrt{-21}}$

$x=\pm{i\sqrt{21}}$ .

Report an Error

Example Question #34 : Solving Quadratic Equations

What are the x-intercepts for f(x)=x^2-3x-4?

Possible Answers:

x=1,-4

x=-1,4

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

x=-1,1

x=4

Correct answer:

x=-1,4

Explanation:

The x-intercepts of a quadratic equation are also the solutions. To find them, factor the quadratic equation. After some trial and error, it can be factored to: (x-4)(x+1) . Set those expressions equal to to get you x-intercepts. Your answers are: x=-1,4 .

Report an Error

Example Question #35 : Solving Quadratic Equations

Find all solutions to the following quadratic equation:

x^2-225=0

Possible Answers:

x=5,10

x=-15,0

$x=\pm15$

x=15,0

Correct answer:

$x=\pm15$

Explanation:

Find all solutions to the following quadratic equation:

x^2-225=0

We can solve the following equation by first bringing the -225 to the other side:

x^2=225

Next, take the square root of both sides.

$x=\sqrt{225}$

Now, you may be tempted to write your answer as just

$x=\sqrt{225}=15$

But, we need to remeber the following is also true

(-15)^2=225

So our answer choice must include both positive and negative 15

$x=\pm15$

Report an Error

Example Question #41 : Solving Quadratic Equations

What are the solutions of x^2-5x+4=0?

Possible Answers:

x=1

x=1,4

x=-1,4

x=1,-4

x=4

Correct answer:

x=1,4

Explanation:

To find the roots, or solutions, of the equation, factor the quadratic. It factors to (x-4)(x-1) . Then, set each expression equal to 0 to get your roots of 1 and 4.

Report an Error

Example Question #42 : Solving Quadratic Equations

What is the x-intercept of f(x)=x^2-1 ?

Possible Answers:

x=1

x=-1

x=1,-1

x=0

Correct answer:

x=1,-1

Explanation:

An x-intercept is the same thing as a root or solution. Therefore, we can set the function equal to 0 and solve for x. $x^2-1=0; x^2=1; x=\pm 1$ .

Report an Error

Example Question #193 : Quadratic Equations And Inequalities

Find the roots of the equation shown below:

4x^3-4x^2-120x

Possible Answers:

6, -5

-6, 5

-6, 0, 5

0, 5, 6

-5, 0, 6

Correct answer:

-5, 0, 6

Explanation:

The first step in finding the root is to factor the polynomial. The common factor in each term is , so extract that from the equation first. 4x(x^2-x-30) . Continue to find the numbers that will multiply to , and add to . If there is no number in front of the variable, it means there is just one of them!

The factors of 30=(1,2,3,5,6,10,15,30) . One of the terms will need to be negative, and in this case it will be the larger number in order to equal . The numbers that work are 5,6 . The factored polynomial would be 4x(x-6)(x+5) . There are three roots for this problem. The first will be 0, because if the is multiplied by , then it will equal 0. The other numbers to fulfill the equation would be 6, -5 . Therefore, the roots are (-5,0,6) .

Report an Error

Example Question #43 : Solving Quadratic Equations

What are the roots of the following equation?

(x+3)(x)

Possible Answers:

x=3, x=-3

x=3, x=0

x=-3

x=3

x=-3, x=0

Correct answer:

x=-3, x=0

Explanation:

Roots are the values of "x" where your function equals 0. You need to set both equations equal to 0 and then solve for "x." Upon doing so you get:

x=-3, x=0

Report an Error

View Algebra 2 Tutors

Satweka
Certified Tutor

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

View Algebra 2 Tutors

Justin
Certified Tutor

Vanderbilt University, Bachelor, Computer Science, Mathematics, & Philosophy.

View Algebra 2 Tutors

Jack
Certified Tutor

University of Washington-Seattle Campus, Bachelor in Arts, Mathematics. Western Washington University, Master of Science, Mat...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Phoenix, Spanish Tutors in New York City, Chemistry Tutors in Boston, Algebra Tutors in Seattle, ACT Tutors in San Diego, ISEE Tutors in San Diego, GRE Tutors in Chicago, Biology Tutors in Phoenix, Biology Tutors in San Francisco-Bay Area, Statistics Tutors in Boston

Popular Courses & Classes

SSAT Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, GMAT Courses & Classes in Washington DC, GMAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Seattle, SAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Boston, Spanish Courses & Classes in Miami, LSAT Courses & Classes in Washington DC

Popular Test Prep

ACT Test Prep in Philadelphia, ISEE Test Prep in Boston, MCAT Test Prep in New York City, ISEE Test Prep in New York City, GMAT Test Prep in Washington DC, LSAT Test Prep in Denver, ACT Test Prep in Atlanta, MCAT Test Prep in Boston, SAT Test Prep in Chicago, SSAT Test Prep in Atlanta

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

Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #34 : Finding Roots

Example Question #33 : Solving Quadratic Equations

Example Question #34 : Solving Quadratic Equations

Example Question #33 : Finding Roots

Example Question #34 : Solving Quadratic Equations

Example Question #35 : Solving Quadratic Equations

Example Question #41 : Solving Quadratic Equations

Example Question #42 : Solving Quadratic Equations

Example Question #193 : Quadratic Equations And Inequalities

Example Question #43 : Solving Quadratic Equations

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: