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The line represented by which of the following equation does

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The line represented by which of the following equation does [#permalink] New post 25 Aug 2012, 03:20
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The line represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1

A. y = 2x^2+5x+1
B. y = x^2+5x+2
C. y = 3x^2+5x+2
D. y = 3x^2+7x+2
E. y = x^2+7x+1


@Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Jun 2013, 04:52, edited 2 times in total.
Edited the question.
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Re: The line represented by which of the following equation does [#permalink] New post 25 Aug 2012, 03:39
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vinay911 wrote:
The line represented by which of the following equation does not intersect with the line represented by y = 3x2+ 5x+1

a)y = 2x2+ 5x+1

b) y = x2+ 5x+2

c)y = 3x2+ 5x+2

d)y = 3x2+ 7x+2

e)y = x2 + 7x+1


@Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.


Answer C:
Because y=3x^2+5x+2=(3x^2+5x+1)+1 meaning the graph of C (which is a parabola) is that of the given equation, just shifted one unit up. Obviously, the two graphs don't intersect.

How to pick the right answer?
First of all, you can eliminate A and E, because for x=0, they both give the same value y=1, the same for the given expression in the stem.
Then, try to look for the expressions that have most terms in common with the given one. All the graphs of the given expressions are upward parabolas, so try to think when they cannot intersect. One case is the translation (moving the parabola vertically up or down).
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Re: The line represented by which of the following equation does [#permalink] New post 25 Aug 2012, 08:54
EvaJager wrote:
vinay911 wrote:
The line represented by which of the following equation does not intersect with the line represented by y = 3x2+ 5x+1

a)y = 2x2+ 5x+1

b) y = x2+ 5x+2

c)y = 3x2+ 5x+2

d)y = 3x2+ 7x+2

e)y = x2 + 7x+1


@Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.


Answer C:
Because y=3x^2+5x+2=(3x^2+5x+1)+1 meaning the graph of C (which is a parabola) is that of the given equation, just shifted one unit up. Obviously, the two graphs don't intersect.

How to pick the right answer?
First of all, you can eliminate A and E, because for x=0, they both give the same value y=1, the same for the given expression in the stem.
Then, try to look for the expressions that have most terms in common with the given one. All the graphs of the given expressions are upward parabolas, so try to think when they cannot intersect. One case is the translation (moving the parabola vertically up or down).



@EvaJager/Bunuel: How did we conclude that the 2 parabolas (one that is shifted up vertically w.r.t the other) does NOT intersect each other ?
I guess i am missing something basic here.
Thanks!
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Re: The line represented by which of the following equation does [#permalink] New post 25 Aug 2012, 09:06
vinay911 wrote:
EvaJager wrote:
vinay911 wrote:
The line represented by which of the following equation does not intersect with the line represented by y = 3x2+ 5x+1

a)y = 2x2+ 5x+1

b) y = x2+ 5x+2

c)y = 3x2+ 5x+2

d)y = 3x2+ 7x+2

e)y = x2 + 7x+1


@Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.


Answer C:
Because y=3x^2+5x+2=(3x^2+5x+1)+1 meaning the graph of C (which is a parabola) is that of the given equation, just shifted one unit up. Obviously, the two graphs don't intersect.

How to pick the right answer?
First of all, you can eliminate A and E, because for x=0, they both give the same value y=1, the same for the given expression in the stem.
Then, try to look for the expressions that have most terms in common with the given one. All the graphs of the given expressions are upward parabolas, so try to think when they cannot intersect. One case is the translation (moving the parabola vertically up or down).



@EvaJager/Bunuel: How did we conclude that the 2 parabolas (one that is shifted up vertically w.r.t the other) does NOT intersect each other ?
I guess i am missing something basic here.
Thanks!


For the same value of x, we get some y for one expression and y + 1 for the other expression. y cannot be equal to y + 1.
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Re: The line represented by which of the following equation does [#permalink] New post 10 Sep 2012, 14:23
The other way to solve this question is to create a graph for -2,-1,0,1,2.

Now put these values in the option to see which option doesn't intersect.
This solution is not meant for those who are aware of parabola & base shift or twist

Hope it helps
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Re: The line represented by which of the following equation does [#permalink] New post 06 Nov 2012, 09:34
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


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Re: The line represented by which of the following equation does [#permalink] New post 01 Jun 2013, 06:35
manjusu wrote:
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


Cheers,
Suman.



Manju,

concept of slope for lines & parabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
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Re: The line represented by which of the following equation does [#permalink] New post 01 Jun 2013, 07:17
maaadhu wrote:
manjusu wrote:
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


Cheers,
Suman.



Manju,

concept of slope for lines & parabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.



The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.

So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
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Re: The line represented by which of the following equation does [#permalink] New post 02 Jun 2013, 04:58
Expert's post
BangOn wrote:
maaadhu wrote:
manjusu wrote:
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


Cheers,
Suman.



Manju,

concept of slope for lines & parabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.



The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.

So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0



We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.

This CANNOT be transformed to the question: "which of the following parabolas is parallel to the parabola represented by y=3x^2+5x+1." In the wast majority of cases the word "parallel" is used for lines. Well, we can say that concentric circles are parallel, BUT GMAT, as far as I know, uses this word ONLY about the lines. Next, the word "parallel" when used for curves (lines, ...) means that these curves remain a constant distance apart. So strictly speaking two parabolas to be parallel they need not only not to intersect but also to remain constant distance apart. In this case, I must say that this cannot happen. If a curve is parallel (as we defined) to the parabola it won't be quadratic: so curve parallel to a parabola is not a parabola.
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Re: The line represented by which of the following equation does [#permalink] New post 31 Mar 2014, 12:43
Hi all,

Now we see from the statement that y = 3x^2+5x+1 is a parabola.

The y intercept represents the vertex therefore if +1 is replaced by +2 such as in answer choice C the parabola only move upwards but means that it will never intersect with the original equation.

Therefore answer is C

Hope this helps
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Re: The line represented by which of the following equation does [#permalink] New post 19 Jun 2014, 08:41
The line represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1

Calculate Discriminant (D) for each equation :\sqrt{b^2-4ac}

y = 3x^2+5x+1 ==> \sqrt{13} -- cutting Y axis at 1 -- to calculate intercept put x=0
A. y = 2x^2+5x+1 ==> \sqrt{17} -- D > \sqrt{13} means curve is below original curve cutting Y axis at 1 -- cutting at same point.
B. y = x^2+5x+2 ==> \sqrt{17} -- D > \sqrt{13} means curve is below original curve and Y intercept at 2-- cut is unavoidable.
C. y = 3x^2+5x+2 ==> \sqrt{1} -- D < \sqrt{13} means closest to X axis -- cutting y axis at 2 above 1 -- cutting right above on Y axis and curve is also passing above as D = 1.
D. y = 3x^2+7x+2 ==> \sqrt{25} -- D > \sqrt{13} means curve is below original curve and Y intercept at 2-- cut is unavoidable.-- not plotted on attached graph.
E. y = x^2+7x+1 ==> \sqrt{45} -- D > \sqrt{13} means curve is below original curve cutting Y axis at 1 -- cutting at same point.

Refer following graph to relate the nature of equations and value of D.
Attachment:
2014-06-19_1101.jpg
2014-06-19_1101.jpg [ 34.26 KiB | Viewed 292 times ]

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Re: The line represented by which of the following equation does   [#permalink] 19 Jun 2014, 08:41
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