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

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New post 09 Oct 2018, 01:28
1
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A
B
C
D
E

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  25% (medium)

Question Stats:

67% (01:01) correct 33% (01:15) wrong based on 42 sessions

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New post 09 Oct 2018, 17:19
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Bunuel wrote:
Image
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, 17:19
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