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# If f(x) = 4x^2 + px, what is the minimum value of f(x)?

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Math Revolution GMAT Instructor
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If f(x) = 4x^2 + px, what is the minimum value of f(x)?  [#permalink]

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04 Jul 2018, 00:52
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[GMAT math practice question]

If $$f(x) = 4x^2 + px$$, what is the minimum value of $$f(x)$$?

$$1) f(1) = -4$$
$$2) f(2) = 0$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7099 Re: If f(x) = 4x^2 + px, what is the minimum value of f(x)? [#permalink] ### Show Tags 04 Jul 2018, 01:41 MathRevolution wrote: [GMAT math practice question] If $$f(x) = 4x^2 + px$$, what is the minimum value of $$f(x)$$? $$1) f(1) = -4$$ $$2) f(2) = 0$$ Minimum value of $$4x^2+px$$ is at 8x+p=0 or when $$x=\frac{-p}{8}$$ So min value can be found if value of p is known... 1) f(1)=-4 f(x)=4x^2+px so f(1)=4*1^2+p*1=4+p=-4........ p=-8 So min value be at x=-8/-8=1 f(x)=4x^2-8x=4*(1)^2-8*1=-4 Sufficient 2)f(2)=0 f(x)=4x^2+px so f(2)=4*2^2+p*2=16+2p=0....... p=16/(-2)=-8 So min value be at x=-8/-8=1 f(x)=4x^2-8x=4*(1)^2-8*1=-4 Sufficient D _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Senior Manager Joined: 04 Aug 2010 Posts: 310 Schools: Dartmouth College Re: If f(x) = 4x^2 + px, what is the minimum value of f(x)? [#permalink] ### Show Tags 04 Jul 2018, 01:52 3 MathRevolution wrote: [GMAT math practice question] If $$f(x) = 4x^2 + px$$, what is the minimum value of $$f(x)$$? $$1) f(1) = -4$$ $$2) f(2) = 0$$ To determine the minimum value of the graph, we need to know the value of p. Question stem, rephrased: What is the value of p? Statement 1: Substituting $$x=1$$ and $$f(x)=-4$$ into $$f(x) = 4x^2 + px$$, we get: $$-4 = 4(1^2) + p(1)$$ Since we can solve for $$p$$, SUFFICIENT. Statement 2: Substituting $$x=2$$ and $$f(x)=0$$ into $$f(x) = 4x^2 + px$$, we get: $$0 = 4(2^2) + p(2)$$ Since we can solve for $$p$$, SUFFICIENT. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6619 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If f(x) = 4x^2 + px, what is the minimum value of f(x)? [#permalink] ### Show Tags 06 Jul 2018, 00:41 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 1 variable (p) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) Since $$f(1) = -4,$$ we have $$4 + p = -4$$ and p = $$-8.$$ $$f(x) = 4x^2 -8x = 4( x^2 - 2x + 1 - 1 ) = 4(x-1)^2 – 4.$$ The minimum of $$f(x)$$ is $$-4$$. Condition 1) is sufficient. Condition 2) Since $$f(2) = 0$$, we have $$16 + 2p = 0$$ and $$p = -8.$$ $$f(x) = 4x^2 -8x = 4( x^2 - 2x + 1 - 1 ) = 4(x-1)^2 – 4.$$ The minimum of $$f(x)$$ is $$-4.$$ Condition 2) is sufficient. Therefore, D is the answer. Answer: D Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2). If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If f(x) = 4x^2 + px, what is the minimum value of f(x)? &nbs [#permalink] 06 Jul 2018, 00:41
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