The graph of Fx), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of
F(x)?

The required equation of graph f(x) is

Given that,

The graph of f(x), resembles the graph of G(x) = .

We have to find,

Which of the following could be the equation of  f(x).

According to the question,

Function, ,

The graph in the given question figure. It is a parabola with vertex at (0,0).

By the graph predict that Sign of  is positive, that is why the parabola opens up.

General equation of parabola is given by,

Where, a = 1, and vertex (h, k) is (0,0).

The graph of F(x) unknown function opens down ,

Sign of as negative. and the vertex is at (0,-3)

To find the equation of function f(x),

Putting the values of a and vertex coordinates,

The equation of parabola become:

Hence, The required equation of f(x) is .

For more information about Parabola click the link given below.

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Correct answer is:

C.

Step-by-step explanation:

We are given a function:

The graph of is also shown in the given question figure.

It is a parabola with vertex at (0,0).

Sign of is positive, that is why the parabola opens up.

General equation of parabola is given as:

Here, in G(x), a = 1

Vertex (h,k) is (0,0).

As seen from the question figure,

The graph of F(x) opens down that is why it will have:

Sign of as negative. i.e.

And vertex is at (0,-3)

Putting the values of a and vertex coordinates,

Hence, the equation of parabola will become:

The correct answer is:

C.