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# Does the curve y=b(x-2)^2+c lie completely above the x-axis?

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Manager
Joined: 15 Dec 2015
Posts: 120
GMAT 1: 660 Q46 V35
GPA: 4
WE: Information Technology (Computer Software)
Does the curve y=b(x-2)^2+c lie completely above the x-axis? [#permalink]

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31 Jul 2017, 11:47
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65% (hard)

Question Stats:

46% (00:57) correct 54% (01:16) wrong based on 41 sessions

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Does the curve $$y=b(x-2)^2+c$$ lie completely above the x-axis?

Statement 1: b>0,c<0
Statement 2: b>2,c<2
Intern
Joined: 14 Nov 2012
Posts: 21
Does the curve y=b(x-2)^2+c lie completely above the x-axis? [#permalink]

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28 Oct 2017, 13:38
DH99 wrote:
Does the curve $$y=b(x-2)^2+c$$ lie completely above the x-axis?

Statement 1: b>0,c<0
Statement 2: b>2,c<2

The question is basically about: whether y >0 or not ?
We need to check the sign of the discriminant $$(b^2 - 4ac)$$
If the discriminant >= 0, then the curve will not lie completely above the x-axis.

$$y=b(x-2)^2+c$$
=> $$y = b(x^2 - 4x +4) + c$$
=> $$y = bx^2 - 4bx + 4b + c$$

The discrimimant = $$16b^2 - 4b(4b + c) = -4bc$$

Statement 1: b>0,c<0
=> The discrimimant = -4bc > 0 (Sufficient)

Statement 2: b>2,c<2
With c < 2, it is unsure if c < 0 or c > 0 (Insufficient)
Does the curve y=b(x-2)^2+c lie completely above the x-axis?   [#permalink] 28 Oct 2017, 13:38
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# Does the curve y=b(x-2)^2+c lie completely above the x-axis?

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