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For what value of x between −4 and 4, inclusive, is the value of x2 −

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For what value of x between −4 and 4, inclusive, is the value of x2 −  [#permalink]

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New post 12 Jan 2019, 07:25
For what value of x between −4 and 4, inclusive, is the value of x2 − 10x + 16 the greatest?
(A) −4 (B) −2 (C) 0 (D) 2 (E) 4
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Re: For what value of x between −4 and 4, inclusive, is the value of x2 −  [#permalink]

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New post 12 Jan 2019, 07:45
The answer should be A
You can create facors (x-8)(x-2)
substitute x= -12*-6= 96
or simple the value of
\(x^2\) − 10x + 16 will be max when all terms are positive.
so we are left with -4 and -2 from choices
-4 will yield better results.
Hence ans A
Can you put this in a better format. Follow thsi to post your result
http://gmatclub.com/forum/11-rules-for- ... 33935.html
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Re: For what value of x between −4 and 4, inclusive, is the value of x2 −  [#permalink]

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New post 12 Jan 2019, 08:48
Nums99 wrote:
For what value of x between −4 and 4, inclusive, is the value of x2 − 10x + 16 the greatest?
(A) −4 (B) −2 (C) 0 (D) 2 (E) 4


For such questions, put in the values given in solution into the given equation- \(x^2\)-10x+16

Option (1) putting in -4 will give 72
Option (2) putting in -2 will give 40
Option (3) putting in 0 will give 16
Option (4) putting in 2 will give 0
Option (5) putting in 4 will give 8

the greatest number obtained is in option A (72) when x=-4

Hope it helps!
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Re: For what value of x between −4 and 4, inclusive, is the value of x2 −  [#permalink]

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New post 12 Jan 2019, 12:59
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Hi Nums99,

For future reference, you should post your subject-specific questions in their respective sub-forums. For example, the PS Forum can be found here:

https://gmatclub.com/forum/problem-solving-ps-140/

In addition, there's a pretty good chance that many of the practice questions that you might be interested in have already been posted, so you can search them out (for example, through Google). Here is a post discussing the question you are asking about:

https://gmatclub.com/forum/for-what-val ... 11639.html

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Re: For what value of x between −4 and 4, inclusive, is the value of x2 −  [#permalink]

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New post 24 Feb 2019, 09:08
Nums99 wrote:
For what value of x between −4 and 4, inclusive, is the value of x2 − 10x + 16 the greatest?
(A) −4 (B) −2 (C) 0 (D) 2 (E) 4


Solve this question conceptually. I am assuming x2 is actually x^2, which is always non-negative for any value of x. 16 is always positive. Hence we need to worry about only -10x. We can convert this part into a positive number if we have x as negative. Therefore we can rule of option C to E. We are left with -4 and -2. -4 will not only convert -10x to a positive number but also increase its magnitude. Hence Option A is the correct answer.
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Re: For what value of x between −4 and 4, inclusive, is the value of x2 −  [#permalink]

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New post 02 Mar 2019, 09:08
Nums99 wrote:
For what value of x between −4 and 4, inclusive, is the value of x2 − 10x + 16 the greatest?
(A) −4 (B) −2 (C) 0 (D) 2 (E) 4



We see that y = x^2 – 10x + 16 is the graph of an up-opening parabola. We can find the x-intercepts by setting the function equal to 0 and factoring:

x^2 – 10x + 16 = 0

(x – 8)(x - 2) = 0

x = 8 or x = 2

Since the x-intercepts are at 2 and 8, we know that the x-coordinate of the vertex of the parabola (which is a minimum value) is halfway between 2 and 8, which is at x = 5.
For an up-opening parabola, the farther an x-value is from the x-value of the vertex, the greater the value of the function. Thus, from the answer choices given, we see that the x-value that is farthest from x = 5 is -4, and so choice A is correct.

Answer: A
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Re: For what value of x between −4 and 4, inclusive, is the value of x2 −   [#permalink] 02 Mar 2019, 09:08
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