NEW HERE? LEARN MORE
closeclose
Last visit was: 13 May 2024, 15:50 It is currently 13 May 2024, 15:50
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The figure shows the graph y = -2x2. Points A and B are on the graph.

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10155
Own Kudos [?]: 16678 [9]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
The figure shows the graph y = -2x2. Points A and B are on the graph. [#permalink] New post   29 May 2020, 01:13
2
Kudos
7
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

85% (02:04) correct 15% (01:49) wrong based on 105 sessions
Hide Show timer Statistics
[GMAT math practice question]

The figure shows the graph \(y = -2x^2.\) Points \(A\) and \(B\) are on the graph. \(AB\) is parallel to the x-axis, and the length of \(AB\) is \(8\). What is the area of \(△OAB\)?

Attachment:
5.29ps.png
5.29ps.png [ 9.63 KiB | Viewed 3190 times ]


A. \(110\)

B. \(118\)

C. \(128\)

D. \(138\)

E. \(140\)
ShowHide Answer
Official Answer
C
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3136
Own Kudos [?]: 2776 [1]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: The figure shows the graph y = -2x2. Points A and B are on the graph. [#permalink] New post   29 May 2020, 01:26
1
Kudos
Let AB cut Y' at P
Since parabola passes through origin at its lowest point (x,y)=(0,0) it cuts parabola into equal parts.
So, AP = PB = 4
Therefore coordinates of A = (-4,-y) and B = (4,-y)
Now, A is also a point on parabola so A coordinate is satisfying the equation of parabola.
Put x=-4 in equation y=-2x^2
Y=-2(-4)^2
Y=-2(16)
Y=-32
Distance can't be in negative.
So distance between (0,0)&(0,-32) is 32(using distance formula)
So the distance between origin and P (OP) the point at which AB cuts Y' line is 32.
Also, OP is the height of triangle ABO
Now.
Area of ∆ABO = 1/2*Base*height
=> 1/2*32*8
=> 128

Answer is C

Posted from my mobile device
User avatar
B
GunjanMadan1
Intern
Intern
Joined: 06 Apr 2020
Posts: 15
Own Kudos [?]: 14 [1]
Given Kudos: 1
GMAT 1: 730 Q50 V38
Send PM
The figure shows the graph y = -2x2. Points A and B are on the graph. [#permalink] New post   29 May 2020, 02:59
1
Kudos
MathRevolution wrote:
[GMAT math practice question]

The figure shows the graph \(y = -2x^2.\) Points \(A\) and \(B\) are on the graph. \(AB\) is parallel to the x-axis, and the length of \(AB\) is \(8\). What is the area of \(△OAB\)?

Attachment:
5.29ps.png


A. \(110\)

B. \(118\)

C. \(128\)

D. \(138\)

E. \(140\)


Looking at the equation \(y=-2x^2\) , at positive , negative values of x, value of y remains same. Hence distance of A and B from y axis is the same = 8/2 = 4.

For a, x coordinate = -4

as y =-\(2x^2 \)
= -32

This means Point A and B has y coordinate as 32 and hence height of the triangle is 32

Area = \(\frac{1}{2}*8*32\)
=128

Answer : Option C
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10155
Own Kudos [?]: 16678 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The figure shows the graph y = -2x2. Points A and B are on the graph. [#permalink] New post   31 May 2020, 21:18
1
Bookmarks
Expert Reply
=>

Assume \(A(-p, -2p^2)\) and \(B(p, -2p^2)\) on the graph.

The length of \(AB, 2p\) is \(8\) and we have \(2p = 8\) or \(p = 4.\)

The area of the triangle is \((\frac{1}{2})AB·height = (\frac{1}{2})(2p)(2p^2) = 2p^3 = 2·4^3 = 128.\)

Therefore, C is the answer.
Answer: C
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32984
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: The figure shows the graph y = -2x2. Points A and B are on the graph. [#permalink] New post   15 Sep 2022, 01:13
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.
GMAT Club Bot
gmatclubot
Re: The figure shows the graph y = -2x2. Points A and B are on the graph. [#permalink]
15 Sep 2022, 01:13
Moderators:
Bunuel
Math Expert
93243 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions