Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 05 Jun 2020, 12:08

### GMAT Club Daily Prep

#### 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

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

# Does the curve f(x)=y=ax^2+c intersect with the x - axis?

Author Message
TAGS:

### Hide Tags

Director
Joined: 18 Feb 2019
Posts: 783
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

08 Mar 2019, 07:56
6
00:00

Difficulty:

65% (hard)

Question Stats:

50% (01:39) correct 50% (01:46) wrong based on 84 sessions

### HideShow timer Statistics

Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0
Retired Moderator
Joined: 27 Oct 2017
Posts: 1808
WE: General Management (Education)
Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

09 Mar 2019, 07:14
5
I. f(4) > 0
It means a part of the curve is above the x axis at x = 4. But, No info whether
a) the curve is above the x axis

or

b) intersect it in more points.

So, NOT SUFFICIENT.

II. a < 0
It means the parabola, extends downwards but 2 cases are possible.
a) it can intersects

or
b) does not intersect the x axis.

So, NOT SUFFICIENT.

Combing Statement 1 & 2, We get a part of the curve is above the x axis and it extends downwards.
So, It must intersects the x axis.

Hence SUFFICIENT

II. a < 0
kiran120680 wrote:
Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0

Attachment:

1F.jpg [ 12.56 KiB | Viewed 1552 times ]

Attachment:

2F.jpg [ 14.36 KiB | Viewed 1560 times ]

Attachment:

2A.jpg [ 10.34 KiB | Viewed 1541 times ]

Attachment:

1A.jpg [ 10.42 KiB | Viewed 1539 times ]

_________________
##### General Discussion
Manager
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)
Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

09 Mar 2019, 06:53
kiran120680 wrote:
Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0

Could anyone help with the solution?

Manager
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)
Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

09 Mar 2019, 11:24
Thank you gmatbusters!
Retired Moderator
Joined: 27 Oct 2017
Posts: 1808
WE: General Management (Education)
Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

11 Mar 2019, 23:16
2
1
Algebraic approach
Attachments

IMG-20190312-WA0002.jpg [ 69.69 KiB | Viewed 1308 times ]

_________________
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 719
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

11 Mar 2019, 23:27
Algebraic solution attached. Similar to what gmatbusters has outlined.
Attachments

solution.jpeg [ 56.03 KiB | Viewed 1297 times ]

_________________
Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Intern
Status: Preparing
Joined: 12 Apr 2019
Posts: 13
Location: India
Schools: ISB
GPA: 2.9
WE: Marketing (Retail)
Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

07 Aug 2019, 02:16
chetan2u VeritasKarishma Bunuel, could you help with the reasoning for this, please?

Posted from my mobile device
Intern
Joined: 11 May 2019
Posts: 19
Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

07 Aug 2019, 02:17
gmatbusters can u help in clarifying how did u get c as some positive value?

Posted from my mobile device
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10506
Location: Pune, India
Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?  [#permalink]

### Show Tags

07 Aug 2019, 21:58
1
kiran120680 wrote:
Does the curve f(x)=y=ax^2+c intersect with the x - axis?

I. f(4) > 0
II. a < 0

y = ax^2 + c is a quadratic so its graph will be a parabola.

I. f(4) > 0
This means when x = 4, y > 0. So at x = 4, the graph lies above the x axis. It can be done in many ways as shown.

Attachment:

IMG_1843.JPG [ 2.5 MiB | Viewed 840 times ]

II. a < 0
This means that ax^2 is negative so graph is downward opening. Again, it can be done in many ways as shown.
Attachment:

IMG_3399.JPG [ 2.82 MiB | Viewed 841 times ]

Using both, it should lie above x axis at x = 4 but should be downward opening. Hence, only one case is possible. (No 3 in first diagram and no 1 in second diagram, both same)

So the graph will cut x axis.

_________________
Karishma
Veritas Prep GMAT Instructor

Re: Does the curve f(x)=y=ax^2+c intersect with the x - axis?   [#permalink] 07 Aug 2019, 21:58