Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Determine the equation of a parabola and graph a parabola

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

← Previous 1 2 3 4 5 Next →

Example Question #1811 : Pre Calculus

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

Possible Answers:

y= 25x^2+15x+2

y= 25x^2+30x+11

y= 25x^2+15x+11

y= 25x^2+11

y= 25x^2+30x+9

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

Example Question #1812 : Pre Calculus

If the vertex of the parabola is (-1,5 ) , and the y-intercept is , find the equation of the parabola, if possible.

Possible Answers:

$y=-\frac{1}{3}x^2-\frac{2}{3}x+4$

$\textup{There is not enough information to solve for the equation.}$

$y=\frac{1}{5}x^2+x+4$

$y=\frac{1}{3}x^2+4$

y=-x^2-2x+4

Correct answer:

y=-x^2-2x+4

Explanation:

First, write the equation of the parabola in standard form.

y=ax^2+bx+c

Determine the values of the coefficients. The value of the y-intercept is 4, which means that c=4 .

Write the vertex formula.

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

The given point of the vertex is (-1,5 ) , which indicates that:

$-\frac{b}{2a}=-1$

b=2a

Substitute the value of the point and b=2a into the standard form.

5=a(-1)^2+(2a)(-1)+4

5=a-2a+4

1=-a

a=-1

Substitute this value into b=2a to determine the value of .

b=2a=2(-1)= -2

Substitute the values of a,b,c coefficients into the standard form of the parabola.

y=-x^2-2x+4

Report an Error

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

Find the standard form of the equation of the following parabola:

y^2-4y-4x+8=0

Possible Answers:

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

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

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

(y-1)^2=x+4

Correct answer:

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

Explanation:

Recall the standard equation of a horizontal parabola:

(y-k)^2=4p(x-h) , where (h,k) is the vertex and |p| is the focal length.

Start by isolating the terms.

y^2-4y-4x+8=0

y^2-4y=4x-8

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

y^2-4y+4=4x-8+4

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

Factor both sides of the equation to get the standard form of a horizontal parabola.

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

Report an Error

Example Question #1814 : Pre Calculus

Find the standard form of equation of the following parabola:

y^2-2y+36x-35=0

Possible Answers:

(y+1)^2=36(x+1)

(y-1)^2=-36(x-1)

(y-1)^2=36(x-1)

(y+1)^2=-36(x+1)

Correct answer:

(y-1)^2=-36(x-1)

Explanation:

Recall the standard equation of a horizontal parabola:

(y-k)^2=4p(x-h) , where (h,k) is the vertex and |p| is the focal length.

Start by isolating the terms.

y^2-2y+36x-35=0

y^2-2y=-36x+35

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

y^2-2y+1=-36x+35+1

y^2-2y+1=-36x+36

Factor both sides of the equation to get the standard form of a horizontal parabola.

(y-1)^2=-36(x-1)

Report an Error

Example Question #1815 : Pre Calculus

Find the standard form of the equation for the following parabola:

y^2+8y+6x+10=0

Possible Answers:

(y-1)^2=-6(x+4)

(y+4)^2=6(x-1)

(y-4)^2=-6(x-1)

(y+4)^2=-6(x-1)

Correct answer:

(y+4)^2=-6(x-1)

Explanation:

Recall the standard equation of a horizontal parabola:

(y-k)^2=4p(x-h) , where (h,k) is the vertex and |p| is the focal length.

Start by isolating the terms.

y^2+8y+6x+10=0

y^2+8y=-6x-10

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

y^2+8y+16=-6x-10+16

y^2+8y+16=-6x+6

Factor both sides of the equation to get the standard form of a horizontal parabola.

(y+4)^2=-6(x-1)

Report an Error

Example Question #1816 : Pre Calculus

Find the standard form of the equation for the following parabola:

$x^2-14x-\frac{1}{2}y+47=0$

Possible Answers:

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

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

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

$(x-7)^2=\frac{1}{2}(y-8)$

Correct answer:

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

Explanation:

Recall the standard equation of a vertical parabola:

(x-h)^2=4p(y-k) , where (h,k) is the vertex and |p| is the focal length.

Start by isolating the terms.

$x^2-14x-\frac{1}{2}y+47=0$

$x^2-14x=\frac{1}{2}y-47$

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

$x^2-14x+49=\frac{1}{2}y-47+49$

$x^2-14x+49=\frac{1}{2}y+2$

Factor both sides of the equation to get the standard form of a vertical parabola.

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

Report an Error

Example Question #1817 : Pre Calculus

Find the standard form of the equation for the following parabola:

$x^2+6x-\frac{1}{4}y+5=0$

Possible Answers:

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

(x+3)^2=4(y-1)

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

$(x-3)^2=\frac{1}{4}(y-8)$

Correct answer:

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

Explanation:

Recall the standard equation of a vertical parabola:

(x-h)^2=4p(y-k) , where (h,k) is the vertex and |p| is the focal length.

Start by isolating the terms.

$x^2+6x-\frac{1}{4}y+5=0$

$x^2+6x=\frac{1}{4}y-5$

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

$x^2+6x+9=\frac{1}{4}y-5+9$

$x^2+6x+9=\frac{1}{4}y+4$

Factor both sides of the equation to get the standard form of a vertical parabola.

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

Report an Error

Example Question #1818 : Pre Calculus

Find the standard form of the equation for the following parabola:

x^2-20x-24y+28=0

Possible Answers:

(x+10)^2=24(y+2)

(x-10)^2=24(y+3)

(x+10)^2=24(y-1)

(x-10)^2=24(y-3)

Correct answer:

(x-10)^2=24(y+3)

Explanation:

Recall the standard equation of a vertical parabola:

(x-h)^2=4p(y-k) , where (h,k) is the vertex and |p| is the focal length.

Start by isolating the terms.

x^2-20x-24y+28=0

x^2-20x=24y-28

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

x^2-20x+100=24y-28+100

x^2-20x+100=24y+72

Factor both sides of the equation to get the standard form of a vertical parabola.

(x-10)^2=24(y+3)

Report an Error

Example Question #1819 : Pre Calculus

Find the standard form of the equation of a parabola with the following equation:

x^2-18x+100y-119=0

Possible Answers:

(x-2)^2=100(y-9)

(x-9)^2=-100(y-2)

(x-9)^2=-100(y+2)

(x+2)^2=-100(y-9)

Correct answer:

(x-9)^2=-100(y-2)

Explanation:

Recall the standard equation of a vertical parabola:

(x-h)^2=4p(y-k) , where (h,k) is the vertex and |p| is the focal length.

Start by isolating the terms.

x^2-18x+100y-119=0

x^2-18x=-100y+119

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

x^2-18x+81=-100y+119+81

x^2-18x+81=-100y+200

Factor both sides of the equation to get the standard form of a vertical parabola.

(x-9)^2=-100(y-2)

Report an Error

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

Find the standard form of the equation of a parabola that has its focus at (1, 4) and its directerix at y=-2 .

Possible Answers:

(x-1)^2=12(x-2)

(x-1)^2=12(y-1)

(x+1)^2=12(y+1)

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

Correct answer:

(x-1)^2=12(y-1)

Explanation:

First, we need to figure out if this is a vertical parabola or a horizontal parabola. Since we need to move down units from the focus to the directerix, we know that this is a vertical parabola.

Recall the standard equation of a vertical parabola:

(x-h)^2=4p(y-k) , where (h,k) is the vertex and |p| is the focal length.

Remember that the distance from the focus to the directerix is 2|p| . Then, |p|=3 .

With this information, we can then figure out the vertex of the parabola. Since this is a vertical parabola, the -coordinate of the focus and the vertex are the same. To find the -coordinate of the vertex, just move down units from the focus. The vertex is then (1, 1) .

Since the focus is above the vertex, we know that p=3 .

Now, from the vertex, we know that h=1 and k=1 .

Now, plug in all the information to write the standard equation for this parabola:

(x-1)^2=12(y-1)

Report an Error

← Previous 1 2 3 4 5 Next →

View Pre-Calculus Tutors

Gerald Joseph
Certified Tutor

University of Notre Dame, Bachelor of Science, Mathematics. Indiana University, Masters in Business Administration, Business ...

View Pre-Calculus Tutors

Michael
Certified Tutor

University of Richmond, Bachelor of Science, Mathematics. Central Connecticut State University, Master of Arts, Mathematics.

View Pre-Calculus Tutors

Erik
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Physics. University of California-San Diego, Master of Scien...

All Precalculus Resources

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

Popular Subjects

English Tutors in Atlanta, ACT Tutors in Miami, Physics Tutors in San Diego, SAT Tutors in Miami, Physics Tutors in Atlanta, MCAT Tutors in Los Angeles, Calculus Tutors in Philadelphia, MCAT Tutors in Washington DC, ACT Tutors in Boston, ISEE Tutors in Philadelphia

Popular Courses & Classes

ACT Courses & Classes in Atlanta, SAT Courses & Classes in Atlanta, ISEE Courses & Classes in Seattle, ISEE Courses & Classes in New York City, SSAT Courses & Classes in Seattle, SSAT Courses & Classes in Atlanta, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Seattle, SSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Miami

Popular Test Prep

LSAT Test Prep in Chicago, LSAT Test Prep in Washington DC, LSAT Test Prep in Los Angeles, ACT Test Prep in New York City, ISEE Test Prep in New York City, SSAT Test Prep in New York City, ACT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Philadelphia, SSAT Test Prep in Houston, ACT Test Prep in Houston

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 : Determine the equation of a parabola and graph a parabola

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1811 : Pre Calculus

Example Question #1812 : Pre Calculus

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

Example Question #1814 : Pre Calculus

Example Question #1815 : Pre Calculus

Example Question #1816 : Pre Calculus

Example Question #1817 : Pre Calculus

Example Question #1818 : Pre Calculus

Example Question #1819 : Pre Calculus

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: