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

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

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

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

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

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

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

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

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

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

:shock:



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

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

:shock:



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

:shock:



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

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

:shock:



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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New post 06 Sep 2017, 05:21
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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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