Question

Graph each function. How is each graph a translation of f(x) = x2 ? y = (x + 3)2 + 4

Answer 1

The graphs of the functions can be transformed, obtaining related functions.
Vertical and horizontal displacements: It is assumed that c is a positive constant, ie c> 0 and y = f (x) then
y = f (x) + c moves the graph c units up.
y = f (x + c) shifts the graph c units to the right.
For this case :
y = f (x) + 4 moves the graph 4 units up.
y = f (x + 3) moves the graph 3 units to the right.
See attached graph.