the graph of f(x)= x^2+3 is translated to produce the graph of g(x)+ (x+2)^2+3. in which direction was the graph of f translated

Question

this is just asking about translations

Answer 1

Anything inside the parentheses moves the graph horizontally, opposite the operation. Because we have + 2, it translates 2 to the left.

 

The +3 already there moves the graph of x² up 3, so g(x) is the graph of x² but with the vertex at (3,-2).