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)?
a. the graph of g(x) is the graph of f(x) stretched vertically and shifted 5 units to the right
b. the graph of g(x) is the graph of f(x) compressed vertically and shifted 5 units down
c. the graph of g(x) is the graph of f(x) compressed vertically and shifted 5 units to the right
d. the graph of g(x) is the graph of f(x) stretched vertically and shifted 5 units down

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

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

Now , shift the graph 5 units down then we get

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

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.