Last visit was: 21 May 2024, 16:08 It is currently 21 May 2024, 16:08
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625630 [21]
Given Kudos: 81918
Send PM
Most Helpful Reply
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4129
Own Kudos [?]: 9308 [7]
Given Kudos: 91
 Q51  V47
Send PM
General Discussion
Intern
Intern
Joined: 29 Apr 2020
Posts: 17
Own Kudos [?]: 11 [2]
Given Kudos: 19
WE:Analyst (Computer Software)
Send PM
Manager
Manager
Joined: 12 Mar 2019
Posts: 191
Own Kudos [?]: 104 [0]
Given Kudos: 105
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
For a quadratic function of the form ax^2 + bx + c where a>0, the minimum value of the function is given by 4ac–b^2/4a

Putting values:
4*1*14 - (6)^2 /4*1 = 20/4 = > 5

Answer C
Intern
Intern
Joined: 21 Apr 2017
Posts: 36
Own Kudos [?]: 22 [0]
Given Kudos: 256
GMAT 1: 560 Q43 V24
GMAT 2: 580 Q44 V25
GMAT 3: 540 Q44 V20
Send PM
What is the minimum possible value of x^2 – 6x + 14? [#permalink]
Bunuel wrote:
What is the minimum possible value of \(x^2 – 6x + 14\)?

A. 0
B. 1
C. 5
D. 6
E. 14


No formula approach.

\(x^2 – 6x + 14\) = \(x^2 – 6x + 8 + 6\) = \(x^2 – 2x - 4x + 8 + 6\) = (x-2) (x-4) + 6

Remember here, \(x\geq{2}\). Now at x = 2,4 the the value will be 6 , but at x=3, the minimum value will be 5.

So Answer is C.
Intern
Intern
Joined: 21 Feb 2019
Posts: 3
Own Kudos [?]: 1 [0]
Given Kudos: 32
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
Think of it as 10+x^2.
For us to get the minimum value, we can only assign x to 0 (x=0).
Since there is no point in assigning a negative number because of the square.
Now let's work on the question.

x^2–6x+14
x^2-6x+9+5
(x^2-2.x.3+3^2)+5
(x-3)^2+5

So, the minimum value here is 5.

ANS is C.
Intern
Intern
Joined: 12 Oct 2019
Posts: 47
Own Kudos [?]: 38 [0]
Given Kudos: 8
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
The minimum value of a quadratic equation occurs at \(\frac{-b}{2a}\)

The minimum value will occur at \(\frac{-(-6)}{2 \times 1} = 3\)

Putting the value \(x = 3\) in the equation \(x^2 – 6x + 14\)

\(3^2 - 6 \times 3 + 14 = 9 + 14 - 18 = 23 - 18 = 5\)

OA, C
Bunuel wrote:
What is the minimum possible value of \(x^2 – 6x + 14\)?

A. 0
B. 1
C. 5
D. 6
E. 14
VP
VP
Joined: 14 Aug 2019
Posts: 1373
Own Kudos [?]: 848 [1]
Given Kudos: 381
Location: Hong Kong
Concentration: Strategy, Marketing
GMAT 1: 650 Q49 V29
GPA: 3.81
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
1
Kudos
b^2-4ac>= 0 ( because factor of x can be found by x = -b+(or-)sqrt ( b^2-4ac)/2a
i can only change value of c to find the minimum value of expression ( x^2–6x+14 )
36-4c>0 --> c=<9 ==> c= 9 for expression to have 0
current value of c is 14
so minimum value of given expression is 14-9 = 5 ( it would be (x-some factor)^2+ 5= 0
Manager
Manager
Joined: 11 Oct 2019
Posts: 77
Own Kudos [?]: 11 [0]
Given Kudos: 2
Send PM
Re: What is the minimum possible value of x^2 – 6x + 14? [#permalink]
x^2–6x+14
= x^2-6x+9+5
= (x-3)^2+5
Minimum value of square term is 0
Therefore minimum value of the expression is 5
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33139
Own Kudos [?]: 829 [0]
Given Kudos: 0
Send PM
Re: What is the minimum possible value of x^2 6x + 14? [#permalink]
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
Re: What is the minimum possible value of x^2 6x + 14? [#permalink]
Moderator:
Math Expert
93373 posts