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# A graph of the function g(x) is shown above. g(x) is defined

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A graph of the function g(x) is shown above. g(x) is defined [#permalink]  12 Oct 2020, 10:08
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Question Stats:

16% (00:42) correct 83% (00:31) wrong based on 6 sessions
Attachment:

GRE A graph of the function.png [ 17.69 KiB | Viewed 226 times ]

A graph of the function $$g(x)$$ is shown above. $$g(x)$$ is defined by which of the following equations?

A. $$g(x)=(x+1)^2-2$$

B. $$g(x)=(x11)^2-2$$

C. $$g(x)=(x+1)^2+2$$

D. $$g(x)=(x-1)^2+2$$

E. $$g(x)=(x-2)^2+1$$

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: A graph of the function g(x) is shown above. g(x) is defined [#permalink]  16 Oct 2020, 00:29
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Quote:
A graph of the function g(x) is shown above. g(x) is defined by which of the following equations?

Step 1: Understanding the question
Vertex form of the Quadratic equation is a$$(x-h)^2$$ + k = 0, where (h,k) are the coordinates of the vertex.

Step 2: Calculation
refer to the attachment
Value of the vertex (h,k) = (1,-2)
Hence quadratic equation is a$$(x-1)^2$$ - 2 = 0
As value of a = 1, as per the options

B is correct
Attachments

GRE A graph of the function (1).png [ 21.7 KiB | Viewed 109 times ]

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Re: A graph of the function g(x) is shown above. g(x) is defined [#permalink]  16 Oct 2020, 05:32
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The given function g(x)

If we plugin values of x in the functions only option B function satisfy the graph

$$g(x) = (x-1)^2 - 2$$

Let, x=0

Plugin the value of x=0 in the function

$$g(0)=(0-1)^2 - 2= -1$$

x=1

$$g(1)=(1-1)^2 - 2= -2$$

x= -0.42

$$g(-.42)=g(-.42-1)^2 - 2=0$$

So, only option B satisfy the graph of the curve(parabola) with vertex @ (1,-2)

Option B
Re: A graph of the function g(x) is shown above. g(x) is defined   [#permalink] 16 Oct 2020, 05:32
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