Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Does the graphical representation of the quadratic function [#permalink]

Show Tags

03 Oct 2012, 00:50

Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

1. a <0 2. c >0

Hi,

In order to find whether y=ax^2 + c intersect the x-axis we need to find whether y=0 is possible to achieve for sure. In short if ax^2 + c =0 can be achieved for sure!

STAT1 a <0 now ax^2 will become negative as a is -ve and x^2 is positive but we dont know the sign of c. if c<=0 then for sure the curve will not intersect x-axis as ax^2 + c will become negative. if c>0 then the curve WILL intersect x-axis for sure as ax^2 + c= 0 will give us atleast one solution.

so, NOT SUFFICIENT.

STAT2 c >0 In this case we do not know the sign on a if a>=0 then we DO Not have a soltuion. if a <0 then we DO have a solution (as explained above)

So, Not Sufficient.

Combining both we have a <0 and c>0 and ax^2 + c =0 will give us atleast one soltuion. So, the curve will intersect x-axis. So, SUFFICIENT!

Hence, asnwer will be C. Hope it helps!
_________________

Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

The question basically asks whether \(y\) can be zero for some value(s) of \(x\). So, whether \(ax^2+c=0\) has real roots. \(ax^2+c=0\) --> \(x^2=-\frac{c}{a}\) --> this equation will have real roots if \(-\frac{c}{a}\geq{0}\).

(1) a < 0. Not sufficient since no info about c. (2) c > 0. Not sufficient since no info about a.

(1)+(2) \(a<0\) and \(c>0\) means that \(-\frac{c}{a}=-\frac{positive}{negative}=-negative=positive>{0}\). Sufficient.

Re: Does the graphical representation of the quadratic function [#permalink]

Show Tags

04 Oct 2012, 12:51

nktdotgupta wrote:

Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

1. a <0 2. c >0

Hi,

In order to find whether y=ax^2 + c intersect the x-axis we need to find whether y=0 is possible to achieve for sure. In short if ax^2 + c =0 can be achieved for sure!

STAT1 a <0 now ax^2 will become negative as a is -ve and x^2 is positive but we dont know the sign of c. if c<=0 then for sure the curve will not intersect x-axis as ax^2 + c will become negative. if c>0 then the curve WILL intersect x-axis for sure as ax^2 + c= 0 will give us atleast one solution.

so, NOT SUFFICIENT.

STAT2 c >0 In this case we do not know the sign on a if a>=0 then we DO Not have a soltuion. if a <0 then we DO have a solution (as explained above)

So, Not Sufficient.

Combining both we have a <0 and c>0 and ax^2 + c =0 will give us atleast one soltuion. So, the curve will intersect x-axis. So, SUFFICIENT!

Hence, asnwer will be C. Hope it helps!

I didnt get above highlighted point..

can u just elaborate it..
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Re: Does the graphical representation of the quadratic function [#permalink]

Show Tags

28 Nov 2013, 09:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Does the graphical representation of the quadratic function [#permalink]

Show Tags

28 Nov 2013, 11:31

The equation ax^2 + c will intersect or touches the x-axis if it has real roots. Discriminant >= 0. Hence, b^2 - 4ac >=0 i.e. -4ac >=0. We can only predict this when we know about the signs of a and c both. Hence C.

Re: Does the graphical representation of the quadratic function [#permalink]

Show Tags

29 Mar 2014, 09:13

Graph approach also works here

Is y = ax^2 + c?

Well, let's see

Statement 1 a<0

Says parabola* is downward sloping but we don't know about the vertex so could or could not intersect 'x' axis.

Insufficient

Statement 2

C>0

So y intercept is positive but vertex could be above x=0, and thus will not have any solutions for 'x'

Insufficient

Both together

So we know that curve is downward sloping and that 'y' intercept is positive therefore it must at least one solution for 'x' therefore this statement is sufficient

For the graph to intersect the x axis y = 0 or ax^2 + c =0 for the above equation to be true x^2 = -c/a

using 1 + 2 we can only tell c/a is negative hence - c/a is positive

but how can we be sure that x^2 = -c/a ? or how can we be sure that ax^2 + c =0

x= 2 , c= 1 and a = -1 here both 1 + 2 is satisfied but ax^2 + c not equal to 0

x= 2 c= 4 and a = -1 here both 1 + 2 is satisfied and ax^2 + c = 0

so we can get both a yes and no depending upon the individual values of C and a it seems,

Is there anything wrong with the above logic

I think you misinterpreted the question. As long as \(-\frac{c}{a}=positive\), y = ax^2 + c will intersect with the x - axis, because in this case \(ax^2+c=0\) will have real solution(s).
_________________

Does the graphical representation of the quadratic equation Y=Ax^2 + C intersect with x-axis? We are required to find x intercept of equation Y=Ax^2+C put y=0 to find value of x intercept 0=Ax^2+C x^2=-C/A x^2 can't have a negative value. so we need to check whether -C/A has a negative or positive sign. If x^2 is positive, then the solution is real and if it is negative then solution is unreal.

statement 1 : A<0 A is negative, but this information is not sufficient to decode on sign of -C/A

statement 2 : C>0 C is positive, but this information is not sufficient to decode on sign of -C/A

1+2 Combined, -C/A has a positive value, so solution is real and Y=Ax^2 + C intersect with x-axis.

Re: Does the graphical representation of the quadratic function [#permalink]

Show Tags

15 Oct 2015, 04:09

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Hey, guys, So, I’ve decided to run a contest in hopes of getting the word about the site out to as many applicants as possible this application season...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...

Whether you’re an entrepreneur, aspiring business leader, or you just think that you may want to learn more about business, the thought of getting your Masters in Business Administration...