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

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Joined: 15 Dec 2015
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GMAT 1: 660 Q46 V35
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Does the curve y=b(x-2)^2+c lie completely above the x-axis?  [#permalink]

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New post 31 Jul 2017, 10:47
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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
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Does the curve y=b(x-2)^2+c lie completely above the x-axis?  [#permalink]

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New post 28 Oct 2017, 12:38
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)
GMAT Club Bot
Does the curve y=b(x-2)^2+c lie completely above the x-axis? &nbs [#permalink] 28 Oct 2017, 12:38
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