76) Parabola DS

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76) Parabola DS

by ern5231 » Wed May 12, 2010 6:39 am
The curve y= ax^2+bx+c passes through the point (1,2). Does it pass through the point (-1,2)
1) For all values f(x)=f(-x)
2) b = 0

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by liferocks » Wed May 12, 2010 7:17 am
From 1
since f(x)=f(-x) and f(1)=2..f(-1)=2..hence the curve passes through (-1,2)..sufficient

From 2
since the curve passes through (1,2)
2=a+b+c or a+c=2 as b=0

now f(-1)=a+c=2,,hence he curve passes through (-1,2)..sufficient

Ans option D
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by iamseer » Wed May 12, 2010 7:19 am
y= ax^2+bx+c passes through the point (1,2)

therefore,
2=a+b+c

we have to determine if
Is 2= a-b+c?

from 2:
b=0
Sufficient

from 1:
for all values, f(x)=f(-x)
ax^2+bx+c = ax^2-bx+c
b=-b
therefore b=0
Sufficient

IMO answer D
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