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carlosego
The correct answer is the option D.

 The explanation is shown below:

 1. As you can see in the figure attached, the blue parabola has the function f(x)=x^2. This is the patern function.  By definition, this is the most basic function of the quadratics functions.

 2. The red parabola is shifted 2 units to the -y axis and is wider than the first one, by multiplying the variable x. Therefore. As you can see, the correct function that represents this parabola is the function of the option D
 3. If you want to verify it, you can give values to x and plot each point on a graph.
If you observe the two graphs you can note that:

a) F(x) is wider than G(x)
This can be obtained by multiplying the function by a value with magnitude less than 1.

b) F(x) is shifted down 
This can be obtained by subtracting a number from the function value.

From the given option, only option D satisfies these conditions.

So, the correct answer is option D