We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Quadratic Functions

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 #481 : Functions And Graphs

Find the center and radius of the circle given the following equation:

$\frac{(x-3)^2}{2}+\frac{(y-6)^2}{2} = 4$

Possible Answers:

c= (3,6), r= 2

$c= (-3,-6), r= 2\sqrt2$

$\textup{The equation does not resemble a circle.}$

$c= (3,6), r= 2\sqrt2$

c= (-3,-6), r= 2

Correct answer:

$c= (3,6), r= 2\sqrt2$

Explanation:

The equation of a circle is in the format:

(x - h)^2 + (y- k)^2 = r^2

where (h,k) is the center and is the radius.

Multiply two on both sides of the equation.

$2[\frac{(x-3)^2}{2}+\frac{(y-6)^2}{2} = 4]$

The equation becomes:

(x-3)^2+(y-6)^2=8

The center is (3,6) .

The radius is $\sqrt8 = 2\sqrt2$ .

The answer is: $c= (3,6), r= 2\sqrt2$

Report an Error

Example Question #42 : Circle Functions

Determine the radius of the circle given by the following function:

x^2-4x+y^2-2x=11

Possible Answers:

Correct answer:

Explanation:

To rewrite the given function as the equation of a circle in standard form, we must complete the square for x and y. This method requires us to use the following general form:

(a+b)^2=a^2+2ab+b^2

To start, we can complete the square for the x terms. We must halve the coefficient of x, square it, and add it to the first two terms:

(-2)^2=4

x^2-4x+4

Now, we can rewrite this as a perfect square, but because we added 4, we must subtract 4 as to not change the original function:

(x-2)^2-4

We do the same procedure for the y terms:

(-1)^2=1

y^2-2x+1

(y-1)^2-1

Rewriting our function, we get

(x-2)^2-4+(y-1)^2-1=11

Moving the constants to the right side, we get the function of a circle in standard form:

(x-2)^2+(y-1)^2=16

Comparing to

(x-h)^2+(y-k)^2=r^2

we see that the radius of the circle is

$\sqrt{16}=4$

Notice that the radius is a distance and can therefore never be negative.

Report an Error

Example Question #491 : Functions And Graphs

$Identify\ the\ center\ and\ radius\ for\ (x+4)^2+(y-2)^2=49$

Possible Answers:

Center: (4,-2); Radius= 49

Center: (-4,2); Radius= 7

Center: (4,-2); Radius= 7

Center: (-4,2); Radius= 49

Correct answer:

Center: (-4,2); Radius= 7

Explanation:

When identifying the center of a circle, take the opposite sign of each value connected to x and y.

$(x+4)^2+(y-2)^2=49\ compare\ with\ the\ general\ equation\ of\ a\ circle: (x-h)^2+(y-k)^2=r^2$

$Changing\ signs\ for\ each\ gives\ us\ a\ center\ of: (-4,2)$

$To\ find\ the\ radius\ we\ set\ r^2=49,$

$take\ square\ root\ of\ both\ sides\ to\ get\ r=7.$

Report an Error

Example Question #91 : Quadratic Functions

What is the center and radius of the following equation, respectively?

(x-6)^2+(y+7)^2 = 2

Possible Answers:

(6,-7);4

(-6,7); 2

$(-6,7); \sqrt2$

(6,-7); 2

$(6,-7); \sqrt2$

Correct answer:

$(6,-7); \sqrt2$

Explanation:

The equation given represents a circle.

(x-h)^2+(y-k)^2=r^2

(h,k) represents the center, and is the radius.

h=6 , k = -7

The center is at: (6,-7)

Set up an equation to solve the radius.

r^2=2

The radius is: $r=\sqrt{2}$

The answer is: $(6,-7); \sqrt2$

Report an Error

Example Question #492 : Functions And Graphs

Which of the following represents the formula of a circle with a radius of centered at (-1,2) ?

Possible Answers:

(x+1)^2+(y-2)^2=4

$(x-1)^2+(y+2)^2=2\sqrt2$

$(x-1)^2+(y+2)^2=\sqrt2$

$(x+1)^2+(y-2)^2=\sqrt2$

(x-1)^2+(y+2)^2=4

Correct answer:

(x+1)^2+(y-2)^2=4

Explanation:

Write the standard form for a circle.

(x-h)^2+(y-k)^2=r^2

The circle is centered at: (h,k)

The radius is: r=2

Substitute all the known values into the formula.

(x-(-1))^2+(y-2)^2=2^2

Simplify this equation.

The answer is: (x+1)^2+(y-2)^2=4

Report an Error

Example Question #1 : Hyperbolic Functions

Which of the following equations represents a vertical hyperbola with a center of (-4, 3) and asymptotes at $y=\pm\, \frac{4}{3}\, x$ ?

Possible Answers:

$\frac{(x+4)^{2}}{9}-\frac{(y-3)^{2}}{16}=1$

$\frac{(y-3)^{2}}{9}-\frac{(x+4)^{2}}{16}=1$

$\frac{(y+3)^{2}}{16}-\frac{(x-4)^{2}}{9}=1$

$\frac{(y-3)^{2}}{16}-\frac{(x+4)^{2}}{9}=1$

Correct answer:

$\frac{(y-3)^{2}}{16}-\frac{(x+4)^{2}}{9}=1$

Explanation:

First, we need to become familiar with the standard form of a hyperbolic equation:

$\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1$

The center is always at (h,k) . This means that for this problem, the numerators of each term will have to contain $(x+4)^{2}$ and $(y-3)^{2}$ .

To determine if a hyperbola opens vertically or horizontally, look at the sign of each variable. A vertical parabola has a positive $y^{2}$ term; a horizontal parabola has a positive $x^{2}$ term. In this case, we need a vertical parabola, so the $y^{2}$ term will have to be positive.

(NOTE: If both terms are the same sign, you have an ellipse, not a parabola.)

The asymptotes of a parabola are always found by the equation $y=\pm\, \frac{b}{a}\, x$ , where is found in the denominator of the $y^{2}$ term and is found in the denominator of the $x^{2}$ term. Since our asymptotes are $y=\pm\, \frac{4}{3}\, x$ , we know that must be 4 and must be 3. That means that the number underneath the $y^{2}$ term has to be 16, and the number underneath the $x^{2}$ term has to be 9.

Report an Error

Example Question #1 : Hyperbolic Functions

What is the shape of the graph depicted by the equation:

$\small \frac{y^2}{9}-\frac{x^2}{4}=1$

Possible Answers:

Parabola

Hyperbola

Circle

Oval

Correct answer:

Hyperbola

Explanation:

The standard equation of a hyperbola is:

$\small \frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

Report an Error

Example Question #3 : Hyperbolic Functions

Express the following hyperbolic function in standard form:

13(y-7)^2-13(x+6)^2=52

Possible Answers:

$\frac{2(y-7)^2}{13}-\frac{2(x+6)^2}{13}=1$

$\frac{(x-7)^2}{4}+\frac{(y+6)^2}{4}=1$

$\frac{(y-7)^2}{4}-\frac{(x+6)^2}{4}=1$

$\frac{(y-7)^2}{13}+\frac{(x+6)^2}{13}=1$

$\frac{(x-7)^2}{52}-\frac{(y+6)^2}{52}=1$

Correct answer:

$\frac{(y-7)^2}{4}-\frac{(x+6)^2}{4}=1$

Explanation:

In order to express the given hyperbolic function in standard form, we must write it in one of the following two ways:

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$

From our formulas for the standard form of a hyperbolic equation above, we can see that the term on the right side of the equation is always 1, so we must divide both sides of the given equation by 52, which gives us:

$\frac{13(y-7)^2}{52}-\frac{13(x+6)^2}{52}=1$

Simplifying, we obtain our final answer in standard form:

$\frac{(y-7)^2}{4}-\frac{(x+6)^2}{4}=1$

Report an Error

Example Question #1 : Hyperbolic Functions

Which of the following answers best represent $2\sinh(x)$ ?

Possible Answers:

e^x+e^-^x

e^x-e^-^x

$\frac{e^x+e^-^x}{2}$

$\frac{e^x-e^-^x}{2}$

$\frac{2}{e^x+e^-^x}$

Correct answer:

e^x-e^-^x

Explanation:

The correct definition of hyperbolic sine is:

$\sinh(x)= \frac{e^x-e^-^x}{2}$

Therefore, by multiplying 2 by both sides we get the following answer,

$2\sinh(x)=e^x-e^-^x$

Report an Error

Example Question #5 : Hyperbolic Functions

Which of the following best represents $\cosh(x)-\sinh(x)$ , if the value of is zero?

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

Find the values of hyperbolic sine and cosine when x is zero. According to the properties:

$\sinh(0)=\frac{e^x-e^{-x}}{2}=\frac{e^0-e^{-0}}{2}=\frac{1-1}{2}=0$

$\cosh(0)= \frac{e^x+e^{-x}}{2}=\frac{e^0+e^{-0}}{2}=\frac{1+1}{2}=\frac{2}{2}=1$

Therefore:

$\cosh(0)-\sinh(0)=1-0=1$

Report an Error

View Algebra 2 Tutors

Chernyeh
Certified Tutor

Purdue University-Main Campus, Bachelor of Science, Business Administration and Management.

View Algebra 2 Tutors

Bhupinder
Certified Tutor

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

View Algebra 2 Tutors

Vinh
Certified Tutor

Concordia University-, Bachelor of Science, Chemistry.

All Algebra II Resources

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

Popular Subjects

Chemistry Tutors in New York City, Physics Tutors in Philadelphia, Statistics Tutors in Phoenix, ACT Tutors in Atlanta, LSAT Tutors in Houston, SAT Tutors in Philadelphia, MCAT Tutors in Atlanta, SSAT Tutors in Miami, Reading Tutors in Philadelphia, SSAT Tutors in Los Angeles

Popular Courses & Classes

ACT Courses & Classes in Seattle, LSAT Courses & Classes in Atlanta, GMAT Courses & Classes in San Diego, ISEE Courses & Classes in Seattle, LSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Miami, GRE Courses & Classes in Seattle, SAT Courses & Classes in Atlanta, GRE Courses & Classes in Phoenix, Spanish Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GRE Test Prep in Denver, ACT Test Prep in New York City, GMAT Test Prep in San Diego, GMAT Test Prep in Washington DC, SAT Test Prep in Denver, GRE Test Prep in Miami, MCAT Test Prep in Philadelphia, GRE Test Prep in Chicago, ACT Test Prep in Phoenix, GMAT 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 Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #481 : Functions And Graphs

Example Question #42 : Circle Functions

Example Question #491 : Functions And Graphs

Example Question #91 : Quadratic Functions

Example Question #492 : Functions And Graphs

Example Question #1 : Hyperbolic Functions

Example Question #1 : Hyperbolic Functions

Example Question #3 : Hyperbolic Functions

Example Question #1 : Hyperbolic Functions

Example Question #5 : Hyperbolic Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: