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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] New post 12 Oct 2020, 10:08
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Question Stats:

14% (00:42) correct 85% (00:37) wrong based on 7 sessions
Attachment:
GRE A graph of the function.png
GRE A graph of the function.png [ 17.69 KiB | Viewed 232 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. \(g(x)=(x-2)^2+1\)

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[Reveal] Spoiler: OA

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Re: A graph of the function g(x) is shown above. g(x) is defined [#permalink] New post 16 Oct 2020, 00:29
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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
GRE A graph of the function (1).png [ 21.7 KiB | Viewed 115 times ]


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Re: A graph of the function g(x) is shown above. g(x) is defined [#permalink] New post 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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