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# Which of the following could be the equation of the parabola in the co

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Which of the following could be the equation of the parabola in the co  [#permalink]

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09 Oct 2018, 00:28
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1
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:02) correct 29% (01:16) wrong based on 38 sessions

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Which of the following could be the equation of the parabola in the coordinate plane above?

(A) $$y = -x - 1$$

(B) $$y = x^2 + 1$$

(C) $$y = -x^2 - 1$$

(D) $$y = –x^2 + 1$$

(E) $$y = -(x - 1)^2$$

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Which of the following could be the equation of the parabola in the co  [#permalink]

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09 Oct 2018, 16:19
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Bunuel wrote:

Which of the following could be the equation of the parabola in the coordinate plane above?

(A) $$y = -x - 1$$

(B) $$y = x^2 + 1$$

(C) $$y = -x^2 - 1$$

(D) $$y = –x^2 + 1$$

(E) $$y = -(x - 1)^2$$

Equation of parabola in Vertex form: $$y=a(x-h)^2+k$$, where (h,k) is the vertex. 'a' is the co-efficient of $$(x-h)^2$$

The parabola opens upward when a>0 and the parabola opens downward when a<0. Here, from the given figure, it is noticed that a<0.
Now, observe from the given figure that the parabola is in vertex form with (h,k)=(0,1). Let's go through each of the options and compare the equations with the vertex form of parabolan to find (h,k). The equation with (h,k)=(0,1) and a<0 would be our final answer.

A. $$y = -x - 1$$; this isn't the equation of a parabola. DISCARD
B. $$y = (x-0)^2 + 1$$; here (h,k)=(0,1) but a>0. DISCARD
C. $$y = -(x-0)^2 + (-1)$$; here (h,k)=(0,-1). DISCARD
D. $$y = -(x-0)^2 + 1$$;here (h,k)=(0,1) and a<0. KEEP. This is our desired equation of the given parabola.
E. $$y = -(x - 1)^2+0$$;here (h,k)=(1,0). DISCARD

Ans. (D)
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Which of the following could be the equation of the parabola in the co   [#permalink] 09 Oct 2018, 16:19
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# Which of the following could be the equation of the parabola in the co

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