We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Parabolic 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 #403 : Functions And Graphs

Find the location of the vertex of the parabola: y=2(3x+3x^2)

Possible Answers:

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

x=-1

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

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

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

Correct answer:

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

Explanation:

Multiply the two through the binomial.

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

Now that this is in the order of the polynomial y=ax^2+bx+c , we can use the vertex formula.

$x=-\frac{b}{2a}$

Substitute the known coefficients.

$x=-\frac{b}{2a} =-\frac{6}{2(6)}=-\frac{1}{2}$

The answer is: $x=-\frac{1}{2}$

Report an Error

Example Question #11 : Parabolic Functions

Find the location of the vertex for the parabola. Is it a max or min?

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

Possible Answers:

$\textup{Min at }x=\frac{2}{3}$

$\textup{Max at }y=\frac{3}{2}$

$\textup{Max at }x=\frac{2}{3}$

$\textup{Max at }x=\frac{3}{2}$

$\textup{Min at }x=\frac{3}{2}$

Correct answer:

$\textup{Max at }x=\frac{3}{2}$

Explanation:

The polynomial is written in the form of: y=ax^2+bx+c

This is the standard form for a parabola.

Write the vertex formula, and substitute the known values:

$x=-\frac{b}{2a}=-\frac{6}{2(-2)} = \frac{6}{4} =\frac{3}{2}$

The vertex is at: $x=\frac{3}{2}$

Since the coefficient of is negative, the curve will open downward, and will have a maximum.

The answer is: $\textup{Max at }x=\frac{3}{2}$

Report an Error

Example Question #411 : Functions And Graphs

A particular parabola has it's vertex at (-5,-5) , and an x-intercept at the origin. Determine the equation of the parabola.

Possible Answers:

None of these

.2x^2+2x=y

x^2+10x=y

x^2+2x=y

x^2+5x=y

Correct answer:

.2x^2+2x=y

Explanation:

General parabola equation:

ax^2+bx+c=y

Vertex formula:

$h=\frac{-b}{2a}$

Where is the value at the vertex.

Combining equations:

ax^2-2ahx+c=y

Plugging in values for vertex:

a(-5)^2-2a(-5)(-5)+c=(-5)

Solving for :

c=25a-5

Returning to:

ax^2+bx+c=y

combining equations:

ax^2+bx+25a-5=y

Plugging in values of given intercept:

a*0^2+b*0+25a-5=0

Solving for

a=.2

Plugging in value:

c=25(.2)-5

c=0

Plugging in values for the vertex:

.2(-5)^2+b(-5)+0=(-5)

5-5b=-5

b=2

Final equation:

.2x^2+2x=y

Report an Error

Example Question #2 : Quadratic Functions

Which of the following functions represents a parabola?

Possible Answers:

$f(x) = \frac{4x^{2}}{x^{3}}$

f(x) = 5

$f(x) = x^{2} - 9$

f(x) = x

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

Correct answer:

$f(x) = x^{2} - 9$

Explanation:

A parabola is a curve that can be represented by a quadratic equation. The only quadratic here is represented by the function $f(x) = x^{2} - 9$ , while the others represent straight lines, circles, and other curves.

Report an Error

Example Question #14 : Quadratic Functions

What is the point of the vertex of the parabola y=3(3-2x)^2-1 ? Is it a maximum or minimum?

Possible Answers:

$( \frac{3}{2},-1), \textup{Maximum}$

$( \frac{3}{2},-1), \textup{Minimum}$

$( \frac{2}{3},\frac{22}{3}), \textup{Maximum}$

$( \frac{2}{3},\frac{22}{3}), \textup{Minimum}$

$( -\frac{3}{2},107), \textup{Maximum}$

Correct answer:

$( \frac{3}{2},-1), \textup{Minimum}$

Explanation:

It is not necessary to FOIL the binomial in order to solve for the vertex. Switch the terms of the quantity (3-2x) , and this equation will be in vertex form:

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

y=3(-2x+3)^2-1

Set the inner quantity equal to zero.

-2x+3 = 0

Subtract three on both sides.

-2x+3 -3= 0-3

-2x=-3

Divide by negative two on both sides.

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

The location of the vertex is at $x = \frac{3}{2}$ .

To determine the point, substitute the value $x = \frac{3}{2}$ back to the original equation.

$y=3(3-2(\frac{3}{2}))^2-1 = 3(3-3)^2-1 = 0-1 = -1$

The point of the vertex is at: $( \frac{3}{2},-1)$

Since this parabola opens upward, the point of the vertex will be a minimum.

The answer is: $( \frac{3}{2},-1), \textup{Minimum}$

Report an Error

Example Question #932 : Algebra Ii

Where is the vertex located for the given function? y=-2x^2-x-1

Possible Answers:

$(-\frac{1}{4},-\frac{5}{8})$

$(-\frac{1}{4},-\frac{7}{8})$

$(-\frac{1}{4},\frac{5}{8})$

$(-\frac{1}{4},-\frac{11}{8})$

$(\frac{1}{4},-\frac{11}{8})$

Correct answer:

$(-\frac{1}{4},-\frac{7}{8})$

Explanation:

Write the vertex formula.

$x=-\frac{b}{2a}$

The given equation is already in standard polynomial form.

a=-2, b=-1, c=-1

Substitute the known values into the formula.

$x=-\frac{b}{2a}=-\frac{-1}{2(-2)} = -\frac{1}{4}$

Substitute this value back into the original equation to determine the y value.

$y=-2(-\frac{1}{4})^2-(-\frac{1}{4})-1$

Simplify this expression.

$y=-2(\frac{1}{16})+\frac{1}{4}-1 = -\frac{1}{8}+\frac{1}{4}-1$

$y=-\frac{1}{8}+\frac{2}{8}-\frac{8}{8}=-\frac{7}{8}$

The vertex is located at: $(-\frac{1}{4},-\frac{7}{8})$

Report an Error

Example Question #11 : Parabolic Functions

Which of these functions represent a parabola?

Possible Answers:

y=5x-4

y=2x^3+2x^2+4

0=3x^2+7-y

y^2=x^2

Correct answer:

0=3x^2+7-y

Explanation:

A parabola is a curve that is represented by a quadratic function. In this case, the only answer that qualifies is 0=3x^2+7-y . The other answers represent straight lines, and other types of curves.

Report an Error

Example Question #12 : Quadratic Functions

Where is the vertex located for y=5x-3x^2 ?

Possible Answers:

$(\frac{3}{10}, \frac{123}{100})$

$(\frac{5}{6},\frac{25}{12} )$

$(\frac{5}{6},\frac{75}{4} )$

$(-\frac{5}{6},-\frac{25}{4} )$

$(-\frac{5}{6},-\frac{75}{4} )$

Correct answer:

$(\frac{5}{6},\frac{25}{12} )$

Explanation:

Rewrite the equation in standard polynomial form.

y=ax^2+bx+c

y=-3x^2+5x

a=-3, b=5, c=0

Write the vertex formula and substitute the known coefficients.

$x=-\frac{b}{2a} = -\frac{5}{2(-3)} = \frac{5}{6}$

The x-value of the vertex is $\frac{5}{6}$ .

Substitute this value back to the original equation.

$y=-3(\frac{5}{6})^2+5(\frac{5}{6})$

$y=-3(\frac{5}{6})(\frac{5}{6})+5(\frac{5}{6})$

$y=-\frac{25}{12}+\frac{25}{6} = -\frac{25}{12}+\frac{25(2)}{6(2)} =-\frac{25}{12}+\frac{50}{12}$

$y=\frac{25}{12}$

The vertex is located at: $(\frac{5}{6},\frac{25}{12} )$

Report an Error

Example Question #13 : Quadratic Functions

Determine the vertex given the function: y=3x^2-6

Possible Answers:

$\left(-\frac{1}{2}, \frac{21}{4}\right)$

(2,6)

(-2,6)

$\left(\frac{1}{2}, \frac{21}{4}\right)$

(0,-6)

Correct answer:

(0,-6)

Explanation:

The parabola is provided in the form of y=ax^2+bx+c .

Notice that the variable in this equation is zero.

This means that:

$x=-\frac{b}{2a} = 0$

Substitute this value back into the original equation y=3x^2-6 to determine the y-value.

y=3(0)^2-6

y=-6

The vertex is located at: (0,-6)

Report an Error

Example Question #3 : Graphing Quadratic Functions

All of the following are equations of down-facing parabolas EXCEPT:

Possible Answers:

$y = -x^{2}$

$y = -6(x-4)^{2} -6$

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

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

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

Correct answer:

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

Explanation:

A parabola that opens downward has the general formula

$y = -(x-a)^{2} + b$ ,

as the negative sign in front of the (x-a) term makes flips the parabola about the horizontal axis.

By contrast, a parabola of the form $x = y^{2}$ rotates about the vertical axis, not the horizontal axis.

Therefore, $x = 2(y+3)^{2} -5$ is not the equation for a parabola that opens downward.

Report an Error

View Algebra 2 Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Algebra II Resources

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

Popular Subjects

Calculus Tutors in Philadelphia, LSAT Tutors in Philadelphia, Computer Science Tutors in Seattle, English Tutors in San Diego, Physics Tutors in Philadelphia, SAT Tutors in Denver, Reading Tutors in Houston, Chemistry Tutors in Seattle, Statistics Tutors in Washington DC, SAT Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in New York City, Spanish Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, GMAT Courses & Classes in Miami, SSAT Courses & Classes in Seattle, SSAT Courses & Classes in New York City, MCAT Courses & Classes in San Diego, SSAT Courses & Classes in Phoenix, SSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

LSAT Test Prep in Los Angeles, SAT Test Prep in Boston, SSAT Test Prep in Miami, SSAT Test Prep in New York City, GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in Atlanta, ISEE Test Prep in New York City, ACT Test Prep in Miami, SAT Test Prep in New York City, SAT Test Prep in Washington DC

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 : Parabolic Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #403 : Functions And Graphs

Example Question #11 : Parabolic Functions

Example Question #411 : Functions And Graphs

Example Question #2 : Quadratic Functions

Example Question #14 : Quadratic Functions

Example Question #932 : Algebra Ii

Example Question #11 : Parabolic Functions

Example Question #12 : Quadratic Functions

Example Question #13 : Quadratic Functions

Example Question #3 : Graphing Quadratic Functions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: