Suppose that F(x) = x^2 and G(x) = 2x^2-5. Which statement best compares the graph G(x) with the graph of F(x)?

AThe graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units to the right
BThe graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down
CThe graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units to the right
DThe graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down

I believe the correct answer from the choices listed above is option D. The graph G(x) as compared to the graph of F(x) would be that the graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down. 2 is a stretch factor and -5 is the shift downwards of the graph. Hope this answers the question.

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lublana lublana · Answer 2 · 2019-11-20T23:46:24-05:00

Answer:

D.The graph G(x) is the graph of F(x) stretched vertically and shifted 5 units down.

Step-by-step explanation:

We are given that

\(F(x)=x^2\)

\(G(x)=2x^2-5\)

We have to find that which statement compares best the graph G(x) with graph of F(x).

Graph of F(x) is the graph of parabola along y- axis with vertex (0,0).

Graph stretched vertically 'a' times by the formula y'=ay

Now, the graph F(x) is stretched vertically 2 times initial graph then

\(F'(x)=2x^2\)

Now , shift the graph 5 units down then we get

\(G(x)=2x^2-5\)

The general equation of parabola along y- axis is given by

\(y=(x-h)^2+k\)

Where (h,k)=Vertex

Compare the graph G(x) with the general equation of parabola then , we get h=0, k=-5

Therefore, vertex of G(x) is at (0,-5).

Hence, the graph G(x) is the graph of F(x) stretched vertically and shifted 5 units down.