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Does the graphical representation of the quadratic function

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Does the graphical representation of the quadratic function [#permalink] New post 03 Oct 2012, 00:20
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Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

(1) a < 0
(2) c > 0
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Re: Does the graphical representation of the quadratic function [#permalink] New post 03 Oct 2012, 00:50
Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

1. a <0
2. c >0

Hi,

In order to find whether y=ax^2 + c intersect the x-axis we need to find whether y=0 is possible to achieve for sure. In short if ax^2 + c =0 can be achieved for sure!

STAT1
a <0
now ax^2 will become negative as a is -ve and x^2 is positive
but we dont know the sign of c.
if c<=0 then for sure the curve will not intersect x-axis as ax^2 + c will become negative.
if c>0 then the curve WILL intersect x-axis for sure as ax^2 + c= 0 will give us atleast one solution.

so, NOT SUFFICIENT.

STAT2
c >0
In this case we do not know the sign on a
if a>=0 then we DO Not have a soltuion.
if a <0 then we DO have a solution (as explained above)

So, Not Sufficient.

Combining both we have
a <0 and c>0 and ax^2 + c =0 will give us atleast one soltuion.
So, the curve will intersect x-axis.
So, SUFFICIENT!

Hence, asnwer will be C.
Hope it helps!
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Re: Does the graphical representation of the quadratic function [#permalink] New post 03 Oct 2012, 03:53
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Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

The question basically asks whether y can be zero for some value(s) of x. So, whether ax^2+c=0 has real roots. ax^2+c=0 --> x^2=-\frac{c}{a} --> this equation will have real roots if -\frac{c}{a}\geq{0}.

(1) a < 0. Not sufficient since no info about c.
(2) c > 0. Not sufficient since no info about a.

(1)+(2) a<0 and c>0 means that -\frac{c}{a}=-\frac{positive}{negative}=-negative=positive>{0}. Sufficient.

Answer: C.

Hope it's clear.
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Re: Does the graphical representation of the quadratic function [#permalink] New post 04 Oct 2012, 12:51
nktdotgupta wrote:
Does the graphical representation of the quadratic function f(x) = y = ax^2 + c intersect with the x - axis?

1. a <0
2. c >0

Hi,

In order to find whether y=ax^2 + c intersect the x-axis we need to find whether y=0 is possible to achieve for sure. In short if ax^2 + c =0 can be achieved for sure!

STAT1
a <0
now ax^2 will become negative as a is -ve and x^2 is positive
but we dont know the sign of c.
if c<=0 then for sure the curve will not intersect x-axis as ax^2 + c will become negative.
if c>0 then the curve WILL intersect x-axis for sure as ax^2 + c= 0 will give us atleast one solution.

so, NOT SUFFICIENT.

STAT2
c >0
In this case we do not know the sign on a
if a>=0 then we DO Not have a soltuion.
if a <0 then we DO have a solution (as explained above)

So, Not Sufficient.

Combining both we have
a <0 and c>0 and ax^2 + c =0 will give us atleast one soltuion.
So, the curve will intersect x-axis.
So, SUFFICIENT!

Hence, asnwer will be C.
Hope it helps!



I didnt get above highlighted point..

can u just elaborate it..
Re: Does the graphical representation of the quadratic function   [#permalink] 04 Oct 2012, 12:51
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