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Geometry

by gmatblood » Sun Nov 06, 2011 11:07 am
If f(x) = ax^2 + bx + c, and a does not equal 0, at what point does the graph of the function f(x) intersect the y-axis?

1)The graph of f(x) intersects the x-axis exactly twice, at (-6, 0) and (-2, 0)
2)a = 2

imo: C
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by shankar.ashwin » Sun Nov 06, 2011 11:38 am
Given, y = ax^2 + bx + c, we need to find value of 'y' when 'x' = 0

When x=0, y = c.

Statement 1:

x= -6 -> 36a - 6b + c =0
x = -2 -> 4a - 2b + c = 0

Cannot solve for 'c' - 3 unknowns

Statement 2:

a = 2 (Not sufficient alone)

Together, 2 unknown 2 equations. C IMO
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by neelgandham » Sun Nov 06, 2011 2:53 pm
If f(x) = ax^2 + bx + c, and a does not equal 0, at what point does the graph of the function f(x) intersect the y-axis?

The curve y = f(x) intersects the y axis at (0,c).We need to find the value of c in order to answer the question

1)The graph of f(x) intersects the x-axis exactly twice, at (-6, 0) and (-2, 0)

x= -6 => 36a - 6b + c =0
x= -2 => 4a - 2b + c = 0 Insufficient !

Common mistake - Committed by a friend of mine while practising

-6 and -2 are the roots of the equation.So, (x+6)*(x+2) = ax^2 + bx + c. i.e. c = 12. IT IS INCORRECT. If -6 is a root of the equation then the expression can be x+6 or 2x+12 or 3x+18 and so on... You will not be able to find the value of c, till you find the value of a

2)a = 2
Insufficient !

1) and 2) Sufficient !

IMO C
Anil Gandham
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