Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Conic Sections

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Which direction does the parabola open?

y=3x^2

Possible Answers:

Downwards

Upwards

Rightwards

Leftwards

Correct answer:

Upwards

Explanation:

For the function

y=ax^2

The parabola opens upwards if a>0

and downards for a<0

Because

3>0

The parabola opens upwards.

Report an Error

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Determine what direction the following parabola opens: y=-5x^2+3x-4

Possible Answers:

$\textup{Upward and downward}$

$\textup{Right}$

$\textup{Upward}$

$\textup{Downward}$

$\textup{Left}$

Correct answer:

$\textup{Downward}$

Explanation:

The standard form for a parabola is in the form: ax^2+bx+c

The coefficient of the term determines whether if the parabola opens upward or downward. Since the term in the function y=-5x^2+3x-4 is a=-5 , the parabola will open downward.

Report an Error

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Determine what direction will the following function open: y=(1-x)(x-2)

Possible Answers:

$\textup{Left}$

$\textup{Right}$

$\textup{Downward}$

$\textup{None of the other answers.}$

$\textup{Upward}$

Correct answer:

$\textup{Downward}$

Explanation:

Use the FOIL method to determine y=(1-x)(x-2) in its standard form for parabolas, which is y=ax^2+bx+c .

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

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

y= x-2-x^2+2x

Regroup the terms.

y=-x^2+3x-2

Since the coefficient of the term is negative, the parabola will open downward.

Report an Error

Example Question #11 : Parabolas

If a parabola has vertex (-7, 5) and focus (-7, 11) , which direction will it open?

Possible Answers:

down

we would need to know the directrix to determine the parabola's direction

left

right

Correct answer:

Explanation:

The focus is above the vertex, which means that the parabola will open up

Report an Error

Example Question #12 : Parabolas

Determine the direction in which the parabola will open. x-y=-2y^2-2

Possible Answers:

Left

The graph is a straight line.

Right

Down

Correct answer:

Left

Explanation:

In order to determine which way this parabola, group the variables in one side of the equation. Add on both sides of the equation to isolate .

x-y=-2y^2-2

x=-2y^2+y-2

Because the equation is in terms of , the parabola will either open left or right. Notice that the coefficient of the y^2 term is negative.

The parabola will open to the left.

Report an Error

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Determine whether the following parabola opens up or down and state how you know.

y=3x^2-4x-198

Possible Answers:

Down, because the linear term is negative.

Up, because the squared term is positive.

Up, because the linear term is negative.

Down, because the constant term is negative.

Correct answer:

Up, because the squared term is positive.

Explanation:

Determine whether the following parabola opens up or down and state how you know.

y=3x^2-4x-198

To determine the direction a parabola opens, we only need to worry about the squared term.

In this case, it is positive, so the parabola opens upward.

The linear term is negative, so the parabola will be to the right of the y-axis.

The constant term is negative, so the parabola will be located below the x-axis.

Report an Error

Example Question #8 : Determine The Equation Of A Parabola And Graph A Parabola

Determine which direction the equation opens: 2x^2+y=4

Possible Answers:

$\textup{Down}$

$\textup{Up}$

$\textup{Left}$

$\textup{Not a parabola.}$

$\textup{Right}$

Correct answer:

$\textup{Down}$

Explanation:

In order to determine how the parabola will open, we will need to rewrite the equation in standard form.

Write the standard form for parabolas.

y=ax^2+bx+c

Subtract -2x^2 from both sides of the equation.

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

y=-2x^2+4

Since the coefficient of the is negative, and the equation is in terms of , the parabola will open downward.

The answer is: $\textup{Down}$

Report an Error

Example Question #2 : Determine The Equation Of A Parabola And Graph A Parabola

Which is the equation for a parabola that opens down?

Possible Answers:

y = -x^3 - x^2 + x - 7

y - x^2 = 3

y = x^2 + 3 x - 2

y = (x-3)^2 + 1

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

Correct answer:

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

Explanation:

The answer is y = -(x+1)^2 - 3 because it is the only degree-2 polynomial with a negative leading coefficient.

Report an Error

Example Question #22 : Parabolas

Express the following equation for a parabola in standard form:

$\frac{x^2-6x}{3}=y+7$

Possible Answers:

$y=\frac{7}{3}x^2+2x+\frac{7}{3}$

$y=-\frac{7}{3}x^2-2x-\frac{7}{3}$

$y=\frac{7(x^2-6x)}{3}$

$y=-\frac{1}{3}x^2+2x-7$

$y=\frac{1}{3}x^2-2x-7$

Correct answer:

$y=\frac{1}{3}x^2-2x-7$

Explanation:

In order to be in standard form, the equation for a parabola must be written in one of the following ways:

y=ax^2+bx+c

x=ay^2+by+c

We can see that our equation has all of the components of the first form above, so now all we must do is some algebra to rearrange the equation and express the function y in terms of x. We start by simplifying the fraction on the left side of the equation, and then we isolate y to give us the equation of the parabola in standard form:

$\frac{x^2-6x}{3}=y+7$

$\frac{1}{3}x^2-2x=y+7$

$y=\frac{1}{3}x^2-2x-7$

Report an Error

Example Question #11 : Determine The Equation Of A Parabola And Graph A Parabola

Rewrite y-2=(5x+3)^2 in standard form.

Possible Answers:

y= 25x^2+15x+11

y= 25x^2+30x+9

y= 25x^2+11

y= 25x^2+30x+11

y= 25x^2+15x+2

Correct answer:

y= 25x^2+30x+11

Explanation:

The standard form of a parabola is y=ax^2+bx+c .

Factorize the right side of y-2=(5x+3)^2 , and simplify.

(5x+3)^2=(5x+3)(5x+3)= 25x^2+30x+9

y-2= 25x^2+30x+9

y= 25x^2+30x+11

Report an Error

View Pre-Calculus Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Mechanical Engineering.

View Pre-Calculus Tutors

Nicholas
Certified Tutor

Salem State University, Bachelor of Science, GIS Technology.

View Pre-Calculus Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Chicago, GMAT Tutors in Houston, Statistics Tutors in Seattle, Chemistry Tutors in Dallas Fort Worth, Biology Tutors in Atlanta, Math Tutors in Seattle, Computer Science Tutors in San Francisco-Bay Area, Reading Tutors in Seattle, Spanish Tutors in Chicago, Math Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Boston, GMAT Courses & Classes in New York City, LSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Los Angeles, ACT Courses & Classes in Los Angeles, SSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in New York City, GMAT Test Prep in Philadelphia, SAT Test Prep in Chicago, GMAT Test Prep in Boston, ACT Test Prep in Los Angeles, SSAT Test Prep in Philadelphia, SAT Test Prep in Washington DC, GRE Test Prep in Houston, SAT Test Prep in Seattle, SSAT Test Prep in Dallas Fort Worth

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

Precalculus : Conic Sections

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Example Question #11 : Parabolas

Example Question #12 : Parabolas

Example Question #1 : Determine The Equation Of A Parabola And Graph A Parabola

Example Question #8 : Determine The Equation Of A Parabola And Graph A Parabola

Example Question #2 : Determine The Equation Of A Parabola And Graph A Parabola

Example Question #22 : Parabolas

Example Question #11 : Determine The Equation Of A Parabola And Graph A Parabola

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: