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If f(x)=a1*x^2+a2*x+a3. Does the equation intersect x axis

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If f(x)=a1*x^2+a2*x+a3. Does the equation intersect x axis [#permalink]

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New post 17 Aug 2008, 05:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If f(x)=a1*x^2+a2*x+a3. Does the equation intersect x axis at two places?

1) f(x)-8 intersect x axis at 2 places.
2) f(x-8) intersect x axis at 2 places.

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 06:28
abhijit_sen wrote:
If f(x)=a1*x^2+a2*x+a3. Does the equation intersect x axis at two places?

1) f(x)-8 intersect x axis at 2 places.
2) f(x-8) intersect x axis at 2 places.


this is the equation of parabola .. if the equation of parabola is ax^2 + bx +c, then it'll intersect x axis at two points if b^2 > 4ac

statement 1 : c for original equation = a3,
c for new parabola that, shich intersects the x axis = a3-8.
wo dont know value of a3, so not suff

statement 2 : f (x-8) = 0, say it intersects the x axis at (m,0) and (n,0)
((x-8) - m)((x-8) - n) = 0
(x - (8+m))(x - (8+n)) = 0
means it'll intersect the x axis at two points .. suff

B

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 06:30

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 06:38
abhijit_sen wrote:
If f(x)=a1*x^2+a2*x+a3. Does the equation intersect x axis at two places?

1) f(x)-8 intersect x axis at 2 places.
2) f(x-8) intersect x axis at 2 places.



If a1<>0, then the function is a parabola symmetrical along vertical axis and will intersect the x axis at two points.
We need check if a1<>0

St1) It only changes the constant of the parabola keeping a1 the same and yet intersects the x axis at two point. So sufficient.
st 2) It only changes the variable value of x. Function still remains the same. So sufficient.

I think D is the answer..

If this is incorrect... :|

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 06:46
bhushangiri wrote:
I disagree, but could be wrong as i often am. If i remember correctly, a3 doesn't affect whether the function is parabola or not. Only a1 does. So regardless of what a3 is, if the function is parabolic, it will have two x intercepts.


we are not checking whether the function is parabola or not, we are just checking the intersection with x axis, and a3 does play a very important role there... :wink:

checkout the link above .. your doubt will be cleared in seconds...

Last edited by durgesh79 on 17 Aug 2008, 06:47, edited 1 time in total.

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 06:47
Ok.. I am wrong.. a3 determines the position... so if a3 bumps up the parabola a few notches, it wont intersect the x axis.
Touche.. :-D

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 06:47
durgesh79 wrote:
bhushangiri wrote:
I disagree, but could be wrong as i often am. If i remember correctly, a3 doesn't affect whether the function is parabola or not. Only a1 does. So regardless of what a3 is, if the function is parabolic, it will have two x intercepts.


we are not checking whether the function is parabola or not, we are just checking the intersection with x axis, and a3 does play a very important role there... :wink:



I got it Don D. a3 affects the position of the curve on the plane... but i realized it before i saw ur post... :wink:

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 14:46
That explorer is really cool. Thanks!

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Re: Intersecting Equation [#permalink]

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New post 17 Aug 2008, 16:24
abhijit_sen wrote:
If f(x)=a1*x^2+a2*x+a3. Does the equation intersect x axis at two places?

1) f(x)-8 intersect x axis at 2 places.
2) f(x-8) intersect x axis at 2 places.


B

You don't have to do math for this one. Just visualize.

You don't have to recognize that this is a parabola, but it helps.

(1) Insufficient

f(x)-8 means that the graph f(x) is shifted down by 8. For example, when f(x) = 0, f(x)-8 = -8 and when f(x) = 1, f(x)-8 = -7

Because we're asked about f(x) intersecting the x-axis, vertical shifting of a function potentially changes the intersection frequency and cannot help you answer the question.

(2) Sufficient

f(x-8) means that the graph is shifted horizontally to the left by 8.

Because we're asked about f(x) intersecting the x-axis, horizontal shifting will never change how many times f(x) intersects with the x-axis.

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Re: Intersecting Equation   [#permalink] 17 Aug 2008, 16:24
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If f(x)=a1*x^2+a2*x+a3. Does the equation intersect x axis

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