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 350,000 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:

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

y = x² - 3x + 6?

Since a (coefficient of x²) is +ve, it's an upward parabola.

y intercept is 6

(1) Line L is parallel to x-axis. Not sufficient, as we don't know where does it intersects the y axis.

(2) Line L passes through the point (0, 16). Not sufficient as we don't know the slope, depending on slope line may intersect parabola at zero or multiple points.

(1) + (2)

Sufficient, lines intersects parabola at only two points i.e. where y = 16.

Re: At how many points does line L intersect with the parabola [#permalink]
02 Feb 2012, 00:31

Expert's post

Smita04 wrote:

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6? (1) Line L is parallel to x-axis. (2) Line L passes through the point (0, 16).

What is the source? You did not specify.... _________________

At how many points does line L intersect with the parabola [#permalink]
02 Feb 2012, 08:19

2

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

Generally a parabola and a line can have 0, 1, or 2 intersection points.

Notice than in our case, since the coefficient of x^2 is positive, then we have an upward parabola, which intersects y-axis at (0, 6). Just to illustrate, below is the graph of y = x^2 - 3x + 6:

Attachment:

parabola.gif [ 3.02 KiB | Viewed 3070 times ]

(1) Line L is parallel to x-axis. All three cases are possible: line L can be below the given parabola (no intersection), line L can go through the vertex (1 intersection) or cross it above the vertex (2 intersections). Not sufficient.

Notice that if it were: line L is parallel to y-axis then we would know that it would cross a parabola at one point, hence in this case the statement would be sufficient.

(2) Line L passes through the point (0, 16). Since (0, 16) is higher than y-intercept of parabola, then line L is "trapped" and must have at least one intersection with parabola (it'll have only one for example if L is x=0). Not sufficient.

(1)+(2) Line L intersect with the parabola at two points. Sufficient.

Re: At how many points does line L intersect with the parabola [#permalink]
23 Aug 2014, 02:35

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: At how many points does line L intersect with the parabola [#permalink]
23 Aug 2014, 14:52

1

This post received KUDOS

Bunuel wrote:

(2) Line L passes through the point (0, 16). Since (0, 16) is higher than y-intercept of parabola, then line L is "trapped" and must have at least one intersection with parabola (it'll have only one for example if L is y=0). Not sufficient.

.

I think the highlight words should be x = 0, instead of y = 0. _________________

......................................................................... +1 Kudos please, if you like my post

Re: At how many points does line L intersect with the parabola [#permalink]
24 Aug 2014, 12:19

Expert's post

vad3tha wrote:

Bunuel wrote:

(2) Line L passes through the point (0, 16). Since (0, 16) is higher than y-intercept of parabola, then line L is "trapped" and must have at least one intersection with parabola (it'll have only one for example if L is y=0). Not sufficient.

.

I think the highlight words should be x = 0, instead of y = 0.

Re: At how many points does line L intersect with the parabola [#permalink]
04 Oct 2014, 00:05

Bunuel wrote:

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

Generally a parabola and a line can have 0, 1, or 2 intersection points.

Notice than in our case, since the coefficient of x^2 is positive, then we have an upward parabola, which intersects y-axis at (0, 6). Just to illustrate, below is the graph of y = x^2 - 3x + 6:

Attachment:

parabola.gif

(1) Line L is parallel to x-axis. All three cases are possible: line L can be below the given parabola (no intersection), line L can go through the vertex (1 intersection) or cross it above the vertex (2 intersections). Not sufficient.

Notice that if it were: line L is parallel to y-axis then we would know that it would cross a parabola at one point, hence in this case the statement would be sufficient.

(2) Line L passes through the point (0, 16). Since (0, 16) is higher than y-intercept of parabola, then line L is "trapped" and must have at least one intersection with parabola (it'll have only one for example if L is x=0). Not sufficient.

(1)+(2) Line L intersect with the parabola at two points. Sufficient.

Answer: C.

Hi Bunuel ,Can you explain preferably thru diagram how line intersects parabola in 0 and 1 way. I am ok with 2 but not 0 and 1. Please explain.

Re: At how many points does line L intersect with the parabola [#permalink]
04 Oct 2014, 02:58

Expert's post

snehamd1309 wrote:

Bunuel wrote:

At how many points does line L intersect with the parabola represented by y = x² - 3x + 6?

Generally a parabola and a line can have 0, 1, or 2 intersection points.

Notice than in our case, since the coefficient of x^2 is positive, then we have an upward parabola, which intersects y-axis at (0, 6). Just to illustrate, below is the graph of y = x^2 - 3x + 6:

Attachment:

The attachment parabola.gif is no longer available

(1) Line L is parallel to x-axis. All three cases are possible: line L can be below the given parabola (no intersection), line L can go through the vertex (1 intersection) or cross it above the vertex (2 intersections). Not sufficient.

Notice that if it were: line L is parallel to y-axis then we would know that it would cross a parabola at one point, hence in this case the statement would be sufficient.

(2) Line L passes through the point (0, 16). Since (0, 16) is higher than y-intercept of parabola, then line L is "trapped" and must have at least one intersection with parabola (it'll have only one for example if L is x=0). Not sufficient.

(1)+(2) Line L intersect with the parabola at two points. Sufficient.

Answer: C.

Hi Bunuel ,Can you explain preferably thru diagram how line intersects parabola in 0 and 1 way. I am ok with 2 but not 0 and 1. Please explain.

Check below:

Attachment:

Untitled.png [ 11.72 KiB | Viewed 580 times ]

Any line which is below the vertex of parabola, for example red line in diagram, won't intersect the parabola. Any vertical line (for example orange line) or line passing through the vertex (green line) will intersect parabola at one point.

Good news for globetrotting MBAs: travel can make you a better leader. A recent article I read espoused the benefits of traveling from a managerial perspective, stating that it...