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

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03 Jun 2008, 22:41
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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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03 Jun 2008, 23:22
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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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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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04 Jun 2008, 00:43
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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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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

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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??

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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

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

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04 Jun 2008, 12:43

buffdaddy 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..

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

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04 Jun 2008, 14:29

fresinha12 wrote:

buffdaddy 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.

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

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05 Jun 2008, 03:28

fresinha12 wrote:

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