Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : How to find the equation of a curve

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : How To Find The Equation Of A Curve

An ellipse passes through points (4, 6) , (10,6), (7, 2), (7, 10) .

Give its equation.

Possible Answers:

$\frac{(x-6)^{2}}{9} + \frac{(y-7)^{2}}{16} = 1$

$\frac{(x +7)^{2}}{16} + \frac{(y+6)^{2}}{9}= 1$

$\frac{(x +7)^{2}}{9} + \frac{(y+6)^{2}}{16} = 1$

$\frac{(x-7)^{2}}{9} + \frac{(y-6)^{2}}{16} = 1$

$\frac{(x-6)^{2}}{16} + \frac{(y-7)^{2}} {9}= 1$

Correct answer:

$\frac{(x-7)^{2}}{9} + \frac{(y-6)^{2}}{16} = 1$

Explanation:

The equation of the ellipse with center (h,k) , horizontal axis of length , and vertical axis of length is

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

(4, 6) and (10,6) are the endpoints of a horizontal line segment with midpoint

$\left ( \frac{4+10}{2}, \frac{6+6}{2} \right )$ , or (7,6)

and length 10-4= 6 .

(7, 2) and (7, 10) are the endpoints of a vertical line segment with midpoint

$\left ( \frac{7+7}{2}, \frac{2+10}{2} \right )$ , or (7,6)

and length 10-2 = 8

Because their midpoints coincide, these are the endpoints of the horizontal axis and vertical axis, respectively, of the ellipse, and the common midpoint (7,6) is the center.

Therefore,

h = 7 and k = 6 ;

2a = 6 and 2b= 8 ; consequently a = 3 and b = 4 .

The equation of the ellipse is

$\frac{(x-7)^{2}}{3^{2}} + \frac{(y-6)^{2}}{4^{2}} = 1$ , or

$\frac{(x-7)^{2}}{9} + \frac{(y-6)^{2}}{16} = 1$

Report an Error

Example Question #512 : Ssat Upper Level Quantitative (Math)

A horizontal parabola on the coordinate plane (0,4) as its only -intercept; its -intercept is (6,0) .

Give its equation.

Possible Answers:

Insufficient information is given to determine the equation.

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

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

$x = \frac{8}{3}y^{2}-\frac{64}{3}y+\frac{128}{3}$

$x = \frac{3}{8} y^{2}-3y+6$

Correct answer:

$x = \frac{3}{8} y^{2}-3y+6$

Explanation:

If a horizontal parabola has only one -intercept, which here is (0,4) , that point doubles as its vertex as well.

The equation of a horizontal parabola, in vertex form, is

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

where (h,k) is the vertex. Set h = 0,k=4 :

$x = a(y-4)^{2}+0$

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

To find , use the -intercept, setting x= 6, y=0 :

$6 = a(0-4)^{2}$

$6 = a( -4)^{2}$

6 = 16a

$a = \frac{6}{16} = \frac{3}{8}$

The equation, in vertex form, is $x = \frac{3}{8}(y-4)^{2}$ . In standard form:

$x = \frac{3}{8}(y^{2}-8y+16)$

$x = \frac{3}{8} y^{2}-3y+6$

Report an Error

Example Question #511 : Ssat Upper Level Quantitative (Math)

A horizontal parabola on the coordinate plane has vertex (-3, -6) ; one of its -intercepts is (0, 4) .

Give its equation.

Possible Answers:

$x = \frac{9}{10} y^{2}+ \frac{27}{5} y+ \frac{81}{10}$

$x = \frac{3}{100} y^{2}+\frac{9}{25} y-\frac{48}{25}$

$x = \frac{6}{49} y^{2}+\frac{36}{49} y-\frac{240}{49}$

$x = \frac{7}{36} y^{2}+ \frac{7}{3} y+7$

Insufficient information is given to determine the equation.

Correct answer:

$x = \frac{3}{100} y^{2}+\frac{9}{25} y-\frac{48}{25}$

Explanation:

The equation of a horizontal parabola, in vertex form, is

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

where (h,k) is the vertex. Set h = -3,k=-6 :

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

$x = a(y+6)^{2}-3$

To find , use the known -intercept, setting x =0, y=4 :

$0 = a(4+6)^{2}-3$

$0 = a\cdot 10^{2}-3$

0 =100 a-3

100a= 3

$a = \frac{3}{100}$

The equation, in vertex form, is $x = \frac{3}{100}(y+6)^{2}-3$ ; in standard form:

$x = \frac{3}{100}(y^{2}+12+36)-3$

$x = \frac{3}{100} y^{2}+\frac{9}{25} y+\frac{27}{25} - \frac{75}{25}$

$x = \frac{3}{100} y^{2}+\frac{9}{25} y-\frac{48}{25}$

Report an Error

Example Question #512 : Ssat Upper Level Quantitative (Math)

A vertical parabola on the coordinate plane has -intercepts (0,2) and (0,6) , and passes through (3, -2) .

Give its equation.

Possible Answers:

$x = \frac{2}{3}y^{2}- \frac{16}{3}y+8$

$x =- \frac{2}{3}y^{2}+ \frac{16}{3}y-8$

$x = -\frac{3}{32} y^{2}+ \frac{3}{4} y- \frac{9}{8}$

Insufficient information is given to determine the equation.

$x = \frac{3}{32} y^{2}- \frac{3}{4} y+ \frac{9}{8}$

Correct answer:

$x = \frac{3}{32} y^{2}- \frac{3}{4} y+ \frac{9}{8}$

Explanation:

A horizontal parabola which passes through (0,2) and (0,6) has as its equation

x = a(y-2)(y-6) .

To find , substitute the coordinates of the third point, setting x=3,y=-2 :

3= a(-2-2)(-2-6)

3= a(-4)(-8)

3= 32a

$a = \frac{3}{32}$

The equation is therefore $x = \frac{3}{32}(y-2)(y-6)$ , which is, in standard form:

$x = \frac{3}{32}(y^{2}-8y+12)$

$x = \frac{3}{32} y^{2}- \frac{3}{4} y+ \frac{9}{8}$

Report an Error

Example Question #515 : Ssat Upper Level Quantitative (Math)

A vertical parabola on the coordinate plane has -intercepts (2,0) and (6,0) , and passes through (3, -2) .

Give its equation.

Possible Answers:

$y = \frac{2}{3}x^{2}-\frac{16}{3}x+8$

$y = - \frac{3}{2}x^{2}+12x-18$

$y = x^{2}-8x+12$

$y = \frac{3}{2}x^{2}-12x+18$

$y =- \frac{2}{3}x^{2}+\frac{16}{3}x-8$

Correct answer:

$y = \frac{2}{3}x^{2}-\frac{16}{3}x+8$

Explanation:

A vertical parabola which passes through (2,0) and (6,0) has as its equation

y = a(x-2)(x-6)

To find , substitute the coordinates of the third point, setting x=3,y=-2 :

-2 = a(3-2)(3-6)

$-2 = a \cdot 1 \cdot (-3)$

-2 = -3a

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

The equation is $y = \frac{2}{3}(x-2)(x-6)$ ; expand to put it in standard form:

$y = \frac{2}{3}(x^{2}-8x+12)$

$y = \frac{2}{3}x^{2}-\frac{16}{3}x+8$

Report an Error

Example Question #12 : How To Find The Equation Of A Curve

A horizontal parabola on the coordinate plane has -intercept (6,0) ; one of its -intercepts is (0, 2) .

Give its equation.

Possible Answers:

$x= y^{2}-5 y+ 6$

$x= -2 y^{2}+y + 6$

Insufficient information is given to determine the equation.

$x = - y^{2}- y+ 6$

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

Correct answer:

Insufficient information is given to determine the equation.

Explanation:

The equation of a horizontal parabola, in standard form, is

$x = ay^{2}+ by + c$

for some real a,b,c .

is the -coordinate of the -intercept, so c=6 , and the equation is

$x = ay^{2}+ by + 6$

Set x=0, y=2 :

$0 = a\cdot 2^{2}+ b \cdot 2 + 6$

0 = 4a+2b + 6

However, no other information is given, so the values of and cannot be determined for certain. The correct response is that insufficient information is given.

Report an Error

Example Question #13 : How To Find The Equation Of A Curve

A vertical parabola on the coordinate plane includes points (-2, 23), (1,5), and (3,13) .

Give its equation.

Possible Answers:

$y = x^{2}+4x -8$

$y = x^{2}-4x+8$

$y = 2x^{2}+10x-7$

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

$y = 2x^{2}-4x+7$

Correct answer:

$y = 2x^{2}-4x+7$

Explanation:

The standard form of the equation of a vertical parabola is

$y=ax^{2}+bx+c$

If the values of and from each ordered pair are substituted in succession, three equations in three variables are formed:

$a\cdot (-2)^{2}+b(-2)+c = 23$

4a-2b+c = 23

$a\cdot 1^{2}+b \cdot 1+c = 5$

a+b+c = 5

$a\cdot 3^{2}+b \cdot 3+c =13$

9a+3b+c = 13

The system

4a-2b+c = 23

a+b+c = 5

9a+3b+c = 13

can be solved through the elimination method.

First, multiply the second equation by and add to the third:

9a+3b+c =13

$\underline{ -a-b-c \; \; \; =- 5 }$

8a+2b

Next, multiply the second equation by and add to the first:

4a-2b+c = 23

$\underline{ -a-b-c \; =- 5 }$

3a-3b =18

Which can be divided by 3 on both sides to yield

a-b = 6

Now solve the two-by-two system

8a+2b = 8

a-b = 6

by substitution:

a = b+ 6

8 (b+6)+2b = 8

8b+48+2b = 8

10b+48 = 8

10b= -40

b= -4

Back-solve:

a-(-4) = 6

a+4= 6

a =2

Back-solve again:

2+(-4)+c = 5

-2+c=5

c=7

The equation of the parabola is therefore

$y = 2x^{2}-4x+7$ .

Report an Error

Example Question #14 : How To Find The Equation Of A Curve

A vertical parabola on the coordinate plane shares one -intercept with the line of the equation 2x+4y = 8 , and the other with the line of the equation 4x-2y = 12 . It also passes through (6, -4) . Give the equation of the parabola.

Possible Answers:

$y = -\frac{2}{3}x^{2}+\frac{14}{3}x-8$

$y = \frac{2}{3}x^{2}-\frac{14}{3}x+8$

The correct answer is not among the other responses.

$y = -\frac{3}{2}x^{2}+\frac{21}{2}x-18$

$y = \frac{3}{2}x^{2}- \frac{21}{2}x+18$

Correct answer:

$y = -\frac{2}{3}x^{2}+\frac{14}{3}x-8$

Explanation:

First, find the -intercepts—the points of intersection with the -axis—of the lines by substituting 0 for in both equations.

2x+4y = 8

2x+4 (0) = 8

2x = 8

x=4

(4,0) is the -intercept of this line.

4x-2y = 12

4x-2 (0)= 12

4x= 12

x= 3

(3,0) is the -intercept of this line.

The parabola has -intercepts at (3,0) and (4,0) , so its equation can be expressed as

y = a(x-3)(x-4)

for some real . To find it, substitute using the coordinates of the third point, setting x= 6, y = -4 :

-4 = a(6-3)(6-4)

$-4 = a \cdot 3 \cdot 2$

-4 = 6 a

$a = \frac{-4}{6} = -\frac{2}{3}$ .

The equation is $y = -\frac{2}{3}(x-3)(x-4)$ , which, in standard form, can be rewritten as:

$y = -\frac{2}{3}(x^{2}-7x+12)$

$y = -\frac{2}{3}x^{2}+\frac{14}{3}x-8$

Report an Error

Example Question #15 : How To Find The Equation Of A Curve

A horizontal parabola on the coordinate plane includes points (-11, -1) (-1,1) , and (10,2) .

Give its equation.

Possible Answers:

$x= -y^{2}-4y+4$

$x=2y^{2}-11y+8$

$x=2y^{2}+5y-8$

$x= y^{2}+2y-4$

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

Correct answer:

$x=2y^{2}+5y-8$

Explanation:

The standard form of the equation of a horizontal parabola is

$x=ay^{2}+by+ c$

If the values of and from each ordered pair are substituted in succession, three equations in three variables are formed:

$a \cdot (-1)^{2}+b \cdot (-1)+ c = -11$

a -b + c = -11

$a \cdot (1)^{2}+b \cdot 1+ c = -1$

a+b + c = -1

$a \cdot (2)^{2}+b \cdot 2+ c = 10$

4a+2b+ c = 10

The three-by-three linear system

a -b + c = -11

a+b + c = -1

4a+2b+ c = 10

can be solved by way of the elimination method.

can be found first, by multiplying the first equation by and add it to the second:

a+b + c = -1

$\underline{-a+b - c = 11}$

=10

$2b \div 2 = 10 \div 2$

b = 5

Substitute 5 for in the last two equations to form a two-by-two linear system:

a+5+ c = -1

a+5+ c - 5= -1 - 5

a + c = -6

$4a+2 \cdot 5+ c = 10$

4a+10+ c = 10

4a+10+ c- 10 = 10 - 10

4a +c = 0

The system

a + c = -6

4a +c = 0

can be solved by way of the substitution method;

4a +c = 0

4a +c -4a = 0 -4a

c = -4a

a + (-4a) = -6

-3a = -6

$-3a\div (-3) = -6 \div (-3)$

a = 2

Substitute 2 for in the top equation:

2 + c = -6

2 + c - 2= -6 - 2

c= -8

The equation is $x=2y^{2}+5y-8$ .

Report an Error

View SSAT- Upper Level Tutors

Brooke
Certified Tutor

New York University, Bachelor in Arts, Drama and Dance Teacher Education. Georgia State University, Master of Arts, Communica...

View SSAT- Upper Level Tutors

Carneta
Certified Tutor

Langston University, Bachelor in Arts, Theater Arts.

View SSAT- Upper Level Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in Dallas Fort Worth, Math Tutors in Boston, GMAT Tutors in Denver, Biology Tutors in Boston, ISEE Tutors in Los Angeles, LSAT Tutors in Washington DC, SSAT Tutors in New York City, Physics Tutors in San Francisco-Bay Area, LSAT Tutors in New York City, Calculus Tutors in Dallas Fort Worth

Popular Courses & Classes

Spanish Courses & Classes in Seattle, GRE Courses & Classes in Phoenix, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in San Diego, SAT Courses & Classes in Phoenix, GRE Courses & Classes in Seattle, MCAT Courses & Classes in Miami, ISEE Courses & Classes in Chicago, MCAT Courses & Classes in Denver, GMAT Courses & Classes in Washington DC

Popular Test Prep

MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Boston, SAT Test Prep in Washington DC, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Philadelphia, ISEE Test Prep in Phoenix, GRE Test Prep in New York City, GRE Test Prep in Los Angeles, SSAT Test Prep in Philadelphia, ACT Test Prep in Phoenix

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

SSAT Upper Level Math : How to find the equation of a curve

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #11 : How To Find The Equation Of A Curve

Example Question #512 : Ssat Upper Level Quantitative (Math)

Example Question #511 : Ssat Upper Level Quantitative (Math)

Example Question #512 : Ssat Upper Level Quantitative (Math)

Example Question #515 : Ssat Upper Level Quantitative (Math)

Example Question #12 : How To Find The Equation Of A Curve

Example Question #13 : How To Find The Equation Of A Curve

Example Question #14 : How To Find The Equation Of A Curve

Example Question #15 : How To Find The Equation Of A Curve

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: