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Math Expert V
Joined: 02 Sep 2009
Posts: 57281
The graph above shows the curve of f(x). A, B, and C are three points  [#permalink]

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Difficulty:   15% (low)

Question Stats: 83% (01:10) correct 17% (02:10) wrong based on 47 sessions

### HideShow timer Statistics The graph above shows the curve of f(x). A, B, and C are three points on the graph. If the function f(x) is defined as ax^2, then what are the coordinates of point C?

(1) A = (1.5, 9)
(2) B = (2, 16)

Attachment: 2019-07-19_1157.png [ 65.84 KiB | Viewed 493 times ]

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Manager  S
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: The graph above shows the curve of f(x). A, B, and C are three points  [#permalink]

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2
f(x) = a*x^2

As per question:
1. A = (1.5,9)
=> f(1.5) = a * $$(1.5)^2$$
=> 9 = a * 2.25
=> a = 4
Thus C => 4*$$(2.5)^2$$
Sufficient.

2. B = (2,16)
=> f(2) = a * $$2^2$$
=> 16 = 4*a
=> a =4
Thus C => 4*$$(2.5)^2$$
Sufficient.

IMO the answer is D.

Please hit kudos if you like the solution.
Manager  S
Joined: 18 Dec 2017
Posts: 176
Re: The graph above shows the curve of f(x). A, B, and C are three points  [#permalink]

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RajatVerma1392 wrote:
f(x) = a*x^2

As per question:
1. A = (1.5,9)
=> f(1.5) = a * $$(1.5)^2$$
=> 9 = a * 2.25
=> a = 4
Thus C => 4*$$(2.5)^2$$
Sufficient.

2. B = (2,16)
=> f(2) = a * $$2^2$$
=> 16 = 4*a
=> a =4
Thus C => 4*$$(2.5)^2$$

Sufficient.

IMO the answer is D.

Please hit kudos if you like the solution.

My Question is did you solve it or you knew you will be able to find individually and marked D? Since this is a DS question and not PS
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Please be generous in giving kudos “Practice is the hardest part of learning, and training is the essence of transformation.” ― Ann Voskamp
Software Tester currently in USA ( )
Director  V
Joined: 27 May 2012
Posts: 840
Re: The graph above shows the curve of f(x). A, B, and C are three points  [#permalink]

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RajatVerma1392 wrote:
f(x) = a*x^2

As per question:
1. A = (1.5,9)
=> f(1.5) = a * $$(1.5)^2$$
=> 9 = a * 2.25
=> a = 4
Thus C => 4*$$(2.5)^2$$
Sufficient.

2. B = (2,16)
=> f(2) = a * $$2^2$$
=> 16 = 4*a
=> a =4
Thus C => 4*$$(2.5)^2$$
Sufficient.

IMO the answer is D.

Please hit kudos if you like the solution.

I think in the question it should have been mentioned that "a" is a constant.
_________________
- Stne
Manager  S
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: The graph above shows the curve of f(x). A, B, and C are three points  [#permalink]

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TheNightKing wrote:
RajatVerma1392 wrote:
f(x) = a*x^2

As per question:
1. A = (1.5,9)
=> f(1.5) = a * $$(1.5)^2$$
=> 9 = a * 2.25
=> a = 4
Thus C => 4*$$(2.5)^2$$
Sufficient.

2. B = (2,16)
=> f(2) = a * $$2^2$$
=> 16 = 4*a
=> a =4
Thus C => 4*$$(2.5)^2$$

Sufficient.

IMO the answer is D.

Please hit kudos if you like the solution.

My Question is did you solve it or you knew you will be able to find individually and marked D? Since this is a DS question and not PS

I have solved it, because we need to find one value which is unique and gives the values for C. This is one way to solve questions like these, IMO it does not matter whether it is a DS or PS queston.
Manager  S
Joined: 08 Jan 2018
Posts: 98
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: The graph above shows the curve of f(x). A, B, and C are three points  [#permalink]

### Show Tags

stne wrote:
RajatVerma1392 wrote:
f(x) = a*x^2

As per question:
1. A = (1.5,9)
=> f(1.5) = a * $$(1.5)^2$$
=> 9 = a * 2.25
=> a = 4
Thus C => 4*$$(2.5)^2$$
Sufficient.

2. B = (2,16)
=> f(2) = a * $$2^2$$
=> 16 = 4*a
=> a =4
Thus C => 4*$$(2.5)^2$$
Sufficient.

IMO the answer is D.

Please hit kudos if you like the solution.

I think in the question it should have been mentioned that "a" is a constant.

Yes,It should be stated, but we can also see that for that type of graph there should be one constant that will move the graph in a direction, otherwise if f(x)= $$x^2$$, then that graph should be a parabola, but again we should know whether it is a downward or upward parabola, for that we need some constant. Re: The graph above shows the curve of f(x). A, B, and C are three points   [#permalink] 08 Aug 2019, 01:03
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# The graph above shows the curve of f(x). A, B, and C are three points

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