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# Which of the following could be the equation of the figure above?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Which of the following could be the equation of the figure above?  [#permalink]

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09 Oct 2018, 00:31
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Difficulty:

25% (medium)

Question Stats:

69% (00:50) correct 31% (01:07) wrong based on 56 sessions

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Which of the following could be the equation of the figure above?

(A) $$y = x - 3$$

(B) $$y = 2x^2 - x$$

(C) $$y = x^2 - 3$$

(D) $$y = x^2 + 3$$

(E) $$y = x^3 - 3$$

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Re: Which of the following could be the equation of the figure above?  [#permalink]

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09 Oct 2018, 11:33
The graph is a upward parabola with negative intercept.
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Re: Which of the following could be the equation of the figure above?  [#permalink]

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12 Oct 2018, 19:37
1
Bunuel wrote:

Which of the following could be the equation of the figure above?

(A) $$y = x - 3$$

(B) $$y = 2x^2 - x$$

(C) $$y = x^2 - 3$$

(D) $$y = x^2 + 3$$

(E) $$y = x^3 - 3$$

a) Eliminate options A and E straightaway as they don't belong to parabola family of equations.
b) The given figure is centered or symmetrical about y-axis. Hence the parabola mustn't posses 'x' terms. So, eliminate option (B)
c) The vertex is on the negative y-axis. So, eliminate option (D).

Now, we are left with option (C), $$y=x^2-3$$, which is in the standard form $$y=(x-0)^2+(-3)$$ (Opens upward with y-intercept '-3' and centered on the y-axis)

Ans. (C)
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Re: Which of the following could be the equation of the figure above?  [#permalink]

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12 Oct 2018, 21:06
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It is a parabola with a negative intercept in the y-axis. So the equation must be of the form y=ax^2 - c

Option C matches the equation.
Re: Which of the following could be the equation of the figure above?   [#permalink] 12 Oct 2018, 21:06
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