Last visit was: 17 Jul 2025, 14:47 It is currently 17 Jul 2025, 14:47
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
shreyashid
Joined: 03 Jul 2015
Last visit: 08 Aug 2016
Posts: 19
Own Kudos:
83
 [11]
Given Kudos: 5
Posts: 19
Kudos: 83
 [11]
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 17 Jul 2025
Posts: 11,294
Own Kudos:
41,794
 [5]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,294
Kudos: 41,794
 [5]
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
General Discussion
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,499
 [4]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,499
 [4]
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
User avatar
TeamGMATIFY
Joined: 20 Aug 2015
Last visit: 31 Oct 2016
Posts: 340
Own Kudos:
1,488
 [1]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Expert
Expert reply
GMAT 1: 760 Q50 V44
Posts: 340
Kudos: 1,488
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
shreyashid
If y = x^2 + ax + b, y is minimum when x is:

a) a/b
b) -a/b
c) -a/2
d) -b/2
e) b/a

I tried it by substituting the value of x everywhere For once that is making the problem lengthy, secondly I got stuck . Can anybody help please?

Theory:
Assume the equation to be A\(x^2\) + Bx + C = 0
The minimum value of this equation is found by differentiating it once and putting = 0
Hence 2Ax + B = 0
Therefore the minimum value of this equation will be at x = \(\frac{-B}{{2A}}\)


Coming back to the problem, if we compare x^2 + ax + b with A\(x^2\) + Bx + C = 0
we have A = 1, B = a and C = b

Therefore the minimum value will be at x = -a/2*1 = -a/2

Option C
avatar
senapatitanmay
Joined: 20 Jun 2015
Last visit: 28 Sep 2024
Posts: 3
Given Kudos: 1
Concentration: Finance, Human Resources
GRE 1: Q163 V152
GRE 1: Q163 V152
Posts: 3
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given that:
y=x^2+ax+b.
differentiate this equation and equate to zero.
d(y)/d(x)=2x+a.....1
equate it to zero.
2x+a=0.
x=-a/2.
User avatar
shreyashid
Joined: 03 Jul 2015
Last visit: 08 Aug 2016
Posts: 19
Own Kudos:
Given Kudos: 5
Posts: 19
Kudos: 83
Kudos
Add Kudos
Bookmarks
Bookmark this Post
thanks everyone. the Parabola logic makes it look so simple :)
avatar
sanaexam
Joined: 01 Sep 2016
Last visit: 01 Mar 2017
Posts: 14
Own Kudos:
3
 [1]
Given Kudos: 10
Posts: 14
Kudos: 3
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The minimum value of this equation is found by differentiating it once and putting = 0
Hence 2Ax + B = 0
how did you reach to 2Ax+B=0.Pls explain in detail.srt for the troube
User avatar
ganand
Joined: 17 May 2015
Last visit: 19 Mar 2022
Posts: 198
Own Kudos:
Given Kudos: 85
Posts: 198
Kudos: 3,545
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shreyashid
If y = x^2 + ax + b, y is minimum when x is:

a) a/b
b) -a/b
c) -a/2
d) -b/2
e) b/a

I tried it by substituting the value of x everywhere For once that is making the problem lengthy, secondly I got stuck . Can anybody help please?

Hi,

We can use the method of completing the square to solve this problem.
\(\begin{align*}\\
y &= x^{2} + ax +b\\\\
&= x^{2} + 2\times x \times \frac{a}{2} + \left(\frac{a}{2}\right)^{2} + b - \left(\frac{a}{2}\right)^{2}\\\\
&= \left( x + \frac{a}{2} \right)^{2} + b - \left(\frac{a}{2}\right)^{2}\\
\end{align*}\)

The above expression will have minimum value at \(x = -\frac{a}{2}\).

Thanks.
User avatar
jfranciscocuencag
Joined: 12 Sep 2017
Last visit: 17 Aug 2024
Posts: 229
Own Kudos:
Given Kudos: 132
Posts: 229
Kudos: 136
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here's my solution!

\(y = x^2 + ax + b\)

Considering that \(b^2 - 4ac = 0\)

\(b^2 =4ac\)

Where \(a = x^2\), \(b = a\), \(c = b\) which is constant (so can be just 1).

\(a^2 =4x^2(1)\)

\(\frac{a^2}{4} = x^2\)

\(\frac{a}{2} = x\)

OR

\(\frac{-a}{2} = x\)

After we square root we have +ve and -ve values.

C
avatar
ajmekal
Joined: 22 Mar 2019
Last visit: 03 Sep 2019
Posts: 7
Own Kudos:
Given Kudos: 69
Posts: 7
Kudos: 2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Please remember the basic rule for quadratic equations:
ax^2 + bx + c = y
Here since y is an upward facing parabola if a>0 we'll have minimum value -b/2a (max value reaching +ve infinity), similarly if a<0 we'll have a downward facing parabola with maximum value -b/2a (min value reaches -ve infinity).

Hence the answer will be -b/2a i.e., -a/2
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,440
Own Kudos:
Posts: 37,440
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Math Expert
102605 posts
PS Forum Moderator
697 posts