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# If the parabola represented by f(x) = ax^2 + bx + c passes

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Manager
Joined: 29 Aug 2005
Posts: 239
If the parabola represented by f(x) = ax^2 + bx + c passes  [#permalink]

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03 Jun 2008, 22:41
If the parabola represented by f(x) = ax^2 + bx + c passes through points (-3,0), (0,3) and (5,0) which of the following must be true.

f(-1) > f(-2)
f(1) > f(0)
f(2) > f(1)

A Only I
B Only II
C Only III
D I & II
E II & III

Can you please give me the logic on how to solve these questions
thanks

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Manager
Joined: 28 May 2008
Posts: 90
Re: Parabola question - How to solve this  [#permalink]

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03 Jun 2008, 23:22
1
1
vdhawan1 wrote:
If the parabola represented by f(x) = ax^2 + bx + c passes through points (-3,0), (0,3) and (5,0) which of the following must be true.

f(-1) > f(-2)
f(1) > f(0)
f(2) > f(1)

A Only I
B Only II
C Only III
D I & II
E II & III

Can you please give me the logic on how to solve these questions
thanks

only A is correct.

y=ax^2 + bx + c

and we have 3 co-ordinates (-3,0), (0,3) and (5,0)
substitute them in the equation above
we get 3 equations.
9a-3b+C=0
c=3
25a+5b+c=0

solving these
a=-1/5
b=2/5
c=3

so now the equation becomes -1/5x^2 + 2/5x + 3

now substitute the values
only 1 is satisfied !
A
Manager
Joined: 29 Aug 2005
Posts: 239
Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 00:31
zeenie wrote:
vdhawan1 wrote:
If the parabola represented by f(x) = ax^2 + bx + c passes through points (-3,0), (0,3) and (5,0) which of the following must be true.

f(-1) > f(-2)
f(1) > f(0)
f(2) > f(1)

A Only I
B Only II
C Only III
D I & II
E II & III

Can you please give me the logic on how to solve these questions
thanks

only A is correct.

y=ax^2 + bx + c

and we have 3 co-ordinates (-3,0), (0,3) and (5,0)
substitute them in the equation above
we get 3 equations.
9a-3b+C=0
c=3
25a+5b+c=0

solving these
a=-1/5
b=2/5
c=3

so now the equation becomes -1/5x^2 + 2/5x + 3

now substitute the values
only 1 is satisfied !
A

OK the OA for this says D
can u please have a relook at it

thanks

nonetheless Kudos to u for taking time out to reply to my posts
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Posts: 718
Location: Oxford
Schools: Oxford'10
Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 00:43
1
the best way to solve this is by sketching a quick diagram from the information provided.

The answer D becomes apparent because only 1 and 2 hold true based on the slopes of the parabola
Attachments

para.JPG [ 6.29 KiB | Viewed 6768 times ]

Manager
Joined: 28 May 2008
Posts: 90
Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 01:51
Oh god !! I made such a silly mistake !!
f(1)=3+1/5 and f(0) =3
OBVIOUSLY f(1)>f(0) !!
It is indeed D
SVP
Joined: 29 Mar 2007
Posts: 2379
Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 07:41
vdhawan1 wrote:
If the parabola represented by f(x) = ax^2 + bx + c passes through points (-3,0), (0,3) and (5,0) which of the following must be true.

f(-1) > f(-2)
f(1) > f(0)
f(2) > f(1)

A Only I
B Only II
C Only III
D I & II
E II & III

Can you please give me the logic on how to solve these questions
thanks

D.

Solving we get
9a-3b+c=0
c=3
25a+5b+c=0

a=-1/5, B=2/5, c=3

now we have: f(x)=-1/5*x^2+2/5x+3

Now just plug in -2,-1, 1,0, and 2.
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Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 08:13
how many of you actually did this in under 2 mins??

Director
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Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 10:02
fresinha12 wrote:
how many of you actually did this in under 2 mins??

30 seconds,

the x,y intercepts are given in the questions,,which show its an upsidedown parabola..

then sketched the diagram and figured out mid point (hightest point) will be when x=1.

so the I,II,III options become very easy from then on
Current Student
Joined: 28 Dec 2004
Posts: 3165
Location: New York City
Schools: Wharton'11 HBS'12
Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 12:43
fresinha12 wrote:
how many of you actually did this in under 2 mins??

30 seconds,

the x,y intercepts are given in the questions,,which show its an upsidedown parabola..

then sketched the diagram and figured out mid point (hightest point) will be when x=1.

so the I,II,III options become very easy from then on

how did you calculate the maxima to be 1..

i took the derivative of f(x)=2ax+b...u at the very least need to know the value of a and B to know the maxima..
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Re: Parabola question - How to solve this  [#permalink]

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04 Jun 2008, 14:29
fresinha12 wrote:
fresinha12 wrote:
how many of you actually did this in under 2 mins??

30 seconds,

the x,y intercepts are given in the questions,,which show its an upsidedown parabola..

then sketched the diagram and figured out mid point (hightest point) will be when x=1.

so the I,II,III options become very easy from then on

how did you calculate the maxima to be 1..

i took the derivative of f(x)=2ax+b...u at the very least need to know the value of a and B to know the maxima..

The x-intercepts are given. The maxima will be located at the midpoint of the two intercepts. (-3+5)/2 = 1.
Director
Joined: 14 Oct 2007
Posts: 718
Location: Oxford
Schools: Oxford'10
Re: Parabola question - How to solve this  [#permalink]

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05 Jun 2008, 03:28
fresinha12 wrote:
fresinha12 wrote:
how many of you actually did this in under 2 mins??

30 seconds,

the x,y intercepts are given in the questions,,which show its an upsidedown parabola..

then sketched the diagram and figured out mid point (hightest point) will be when x=1.

so the I,II,III options become very easy from then on

how did you calculate the maxima to be 1..

i took the derivative of f(x)=2ax+b...u at the very least need to know the value of a and B to know the maxima..

the x-coordinate of the maxima will be at midpoint of the intercepts, and we are not interested in teh y-coordinate for this question.
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Re: If the parabola represented by f(x) = ax^2 + bx + c passes  [#permalink]

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06 Sep 2017, 05:21
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--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: If the parabola represented by f(x) = ax^2 + bx + c passes   [#permalink] 06 Sep 2017, 05:21
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