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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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Attachment:
GRE A graph of the function.png
GRE A graph of the function.png [ 17.69 KiB | Viewed 4093 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)=(x−1)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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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
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GRE A graph of the function (1).png
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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
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Re: A graph of the function g(x) is shown above. g(x) is defined [#permalink] New post   13 Jan 2025, 06:24
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A graph of the function g(x) is shown above. g(x) is defined [#permalink]
13 Jan 2025, 06:24
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