GMAT Math : Graphing

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #552 : Geometry

Graph the point (a,b) .

I) (a,b) is in quadrant IV.

II) a^2=49 b^2=36 .

Possible Answers:

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Both statements are needed to answer the question.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

Graph the point (a,b)

I) (a,b) is in quadrant 4

II)

To graph (a,b) we need to know a and b

I) Tells us which quadrant the point is in. In quadrant 4, the x value is positive and the y value must be negative.

II) Lets us find the following:

$a=\pm7$

$b=\pm6$

So the only possible location of (a,b) is (7,-6) .

Therefore, both statements are needed to answer the question.

Report an Error

Example Question #1 : Dsq: Graphing An Exponential Function

Graph the exponential function g(x) .

I) g(x) is a monomial.

II) g(x) has a base of 4.

Possible Answers:

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Both statements are needed to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Correct answer:

Neither statement is sufficient to answer the question. More information is needed.

Explanation:

An exponential function follows the general form of

y=n^x+c

Statement I tells us that there is only one term, so the part of the equation isn't needed for this exponential function.

Statement II tells us that in this case, n=4 .

However, we could have nearly anything as our exponent. We are unable to make an accurate graph of this function, so more information is needed.

Report an Error

Example Question #31 : Graphing

The graph of the function $f(x) = Ax^{2} + Bx +C$ is a parabola. Is this parabola concave upward or is it concave downward?

Statement 1: A = -3

Statement 2: $B^{2} - 4AC = 16$

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Whether the parabola of a quadratic function $f(x) = Ax^{2} + Bx +C$ is concave upward or concave downward depends on one thing and one thing only - whether quadratic coefficient is positive or negative. Statement 1 gives you this information; Statement 2 does not.

Report an Error

Example Question #2 : Dsq: Graphing A Quadratic Function

What is the equation of the line of symmetry of a vertical parabola on the coordinate plane?

Statement 1: The -intercept of the parabola is (0, 6) .

Statement 2: The only -intercept of the parabola is at (3,0) .

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

The line of symmetry of a vertical parabola is the vertical line passing through the vertex. Statement 1 alone is not helpful, since it only gives the -intercept.

Statement 2 alone, however, answers the question. In a parabola with only one -intercept, that -intercept, given in Statement 2 as (3,0) , doubles as the vertex. The vertical line through the vertex, which here is the line with equation x= 3 , is the line of symmetry.

Report an Error

Example Question #3 : Dsq: Graphing A Quadratic Function

The equation of a vertical parabola on the coordinate plane can be written in the form

$f(x)= Ax^{2}+ Bx+C$ , A, B,C real, nonzero.

How many -intercepts does the parabola have - zero, one, or two?

Statement 1: A = B = C

Statement 2: A + B + C = 9

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. The number of -intercepts of the graph of the function $f(x)= Ax^{2}+ Bx+C$ - depends on the sign of the discriminant of the expression, $B^{2}-4AC$ .

If A=B=C , then the discriminant becomes

$A^{2}-4A \cdot A= A^{2}-4 A^{2}= -3A^{2}$

Since in a quadratic equation, is nonzero, $A^{2}$ must be positive, and discriminant $-3A^{2}$ must be negative. This means that the parabola of f(x) has no -intercepts.

We show that Statement 2 alone gives insufficient information by examining two equations: $f(x)= x^{2}+ 7x+1$ and $f(x)= x^{2}+ x+7$ . In both equations, the sum of the coefficients is 9.

In the first equation, the discriminant is

$B^{2}- 4AC = 7^{2}- 4(1)(1)= 49 - 4 = 45$ , a positive value, so the parabola of f(x) has two -intercepts.

In the second equation, however, the discriminant is

$B^{2}- 4AC = 1^{2}- 4(1)(7)= 1-28 = -27$ , a negative value, so the parabola of f(x) has no -intercepts.

Report an Error

Example Question #4 : Dsq: Graphing A Quadratic Function

What is the equation of the line of symmetry of a vertical parabola on the coordinate plane?

Statement 1: The parabola passes through points (-4, 3) and ( 4, 3) .

Statement 2: The parabola passes through the points (-2, 0) and ( 2, 0) .

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. By vertical symmetry, if two points of a parabola have the same -coordinate, the line of symmetry is the vertical line that passes halfway between them. (-4, 3) and ( 4, 3) have the same -coordinate, so the axis of symmetry must be

$x = \frac{-4+4}{2}$ , or x= 0 .

Statement 1 alone is sufficient.

Statement 2 can be proved sufficient using a similar argument.

Report an Error

Example Question #5 : Dsq: Graphing A Quadratic Function

What is the equation of the line of symmetry of a horizontal parabola on the coordinate plane?

Statement 1: The vertex of the parabola has -coordinate 4.

Statement 2: The vertex of the parabola has -coordinate 9.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

The line of symmetry of a horizontal parabola with vertex at (h,k) is the horizonal line of the equation y=k . In other words, the -coordinate of the vertex, which is given in Statement 2 but not Statement 1, is the one and only thing needed.

Report an Error

Example Question #6 : Dsq: Graphing A Quadratic Function

The equation of a vertical parabola on the coordinate plane can be written in the form

$f(x)= Ax^{2}+ Bx+C$ , A, B,C real, nonzero.

Is this parabola concave upward or concave downward?

Statement 1: $B^{2}-4AC =-24$ .

Statement 2: The parabola has -intercept (0,6) .

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. Since $B^{2}-4AC =-24$ - that is, the function $f(x)= Ax^{2}+ Bx+C$ has a negative discriminant - the graph of f(x) has no -intercepts. This alone, however, does not determine whether the parabola is concave upward or concave downward. Also, Statement 2 alone only gives one point of the parabola, thereby providing insufficient information.

Now assume both statements are true. From Statement 2, f(0)= 6 , so the parabola has a point above the -axis. If the parabola is concave downward, then it must cross the -axis, which is impossible as a result of Statement 1. The parabola therefore must be concave upward.

Report an Error

Example Question #32 : Coordinate Geometry

The equation of a vertical parabola on the coordinate plane can be written in the form

$f(x)= Ax^{2}+ Bx+C$ ,

where $A, B,\textup{and }C$ are real, and is a nonzero number.

How many -intercepts does this parabola on the coordinate plane have - zero, one, or two?

Statement 1: $B^{2}=4AC$

Statement 2: A = 2

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. The number of -intercepts(s) of the graph of f(x) depends on the sign of discriminant $B^{2}-4AC$ . By Statement 1, $B^{2}=4AC$ , or, equivalently, $B^{2}-4AC= 0$ , which means that the parabola of f(x) has exactly one -intercept.

Statement 2 alone, that the quadratic coefficient is positive, only establishes that the parabola is concave upward. Therefore, it gives insufficient information.

Report an Error

Example Question #8 : Dsq: Graphing A Quadratic Function

How many -intercepts does a vertical parabola on the coordinate plane have - zero, one, or two?

Statement 1: The vertex of the parabola is (3,3) .

Statement 2: The -intercept of the parabola is (0, 21) .

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

From Statement 1, since the vertex is not on the -axis - its -coordinate is nonzero - the parabola has either zero or two -intercepts. However, with no further information, it is not possible to choose. Statement 2 alone is not helpful since it only gives one point, and no further information about it.

Assume both statements to be true. We can find the equation of the parabola as follows:

A parabola with vertex (h,k) has equation

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

for some nonzero .

From Statement 1, h=k=3 , so the equation becomes

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

Since the parabola passes through (0,21) To find , we substitute 0 for and 21 for :

$21= a(0-3)^{2}+ 3$

$21= a( -3)^{2}+ 3$

9a+3 = 21

9a = 18

a=2

The equation of the parabola is $y= 2(x-3)^{2}+ 3$ .

Now that the equation is known, the -intercept(s) themselves, if any, can be found by substituting 0 for .

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Washington DC, LSAT Tutors in New York City, LSAT Tutors in Seattle, Math Tutors in Phoenix, French Tutors in Los Angeles, French Tutors in Washington DC, Chemistry Tutors in Houston, SAT Tutors in Miami, Statistics Tutors in Boston, Spanish Tutors in Atlanta

Popular Courses & Classes

GMAT Courses & Classes in Houston, GMAT Courses & Classes in San Diego, SSAT Courses & Classes in Boston, GRE Courses & Classes in Boston, SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Seattle, ACT Courses & Classes in Seattle, SSAT Courses & Classes in Phoenix, SSAT Courses & Classes in San Diego, GRE Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in Denver, GMAT Test Prep in Phoenix, SAT Test Prep in Philadelphia, LSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Chicago, MCAT Test Prep in Seattle, MCAT Test Prep in Los Angeles, GMAT Test Prep in San Diego, SAT Test Prep in New York City, LSAT Test Prep in Los Angeles

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)

Email address:
Your name:
Feedback:

GMAT Math : Graphing

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #552 : Geometry

Example Question #1 : Dsq: Graphing An Exponential Function

Example Question #31 : Graphing

Example Question #2 : Dsq: Graphing A Quadratic Function

Example Question #3 : Dsq: Graphing A Quadratic Function

Example Question #4 : Dsq: Graphing A Quadratic Function

Example Question #5 : Dsq: Graphing A Quadratic Function

Example Question #6 : Dsq: Graphing A Quadratic Function

Example Question #32 : Coordinate Geometry

Example Question #8 : Dsq: Graphing A Quadratic Function

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details