Question

What transformations change the graph of f(x) to the graph of g(x)? f(x)=x^2 g(x)=(x+3)^2-7

The graph of g is the graph of f translated to the right 3 units and up 7 units
The graph of g is the graph of f translated to the left 3 units and down 7 units
The graph of g is the graph of f translated up 3 units and to the left 7 units
The graph of g is the graph of f translated down 3 units and to the right 7 units

Answer 1

The graph of g is the graph of f translated to the left 3 units and down 7 units

Explanation:

As you can see, the F(X) graph has its origin on (0,0) since when X is equal to 0, Y will be equal as 0 as well, so having both quadratic graphs, we just have to see how the graph is translated, in this case you just have to make x=0, when X is equal to 0 on g(x) Y=-7, so the graph will be translated 7 units down, the only option you have that has the graph tranlated 7 units down is option 2:"The graph of g is the graph of f translated to the left 3 units and down 7 units"

And that is your correct answer.

Answer 2

The graph of g is the graph of f translated to the left 3 units and down 7 units .