Find the rule and the graph of the function whose graph can be obtained by performing the translation 3 units right and 4 units up on the parent function f(x)=x^2

Answer 1

y=x^2 translated 3 to the right gives

y=(x-3)^2, the vertex shifts from (0,0) to (3,0)

translate it 4 up by adding 4

y=(x-3)^2 + 4, this shifts the vertex up to (3,4)

f(x) = (x-3)^2 + 4 or call it

g(x) = (x-3)^2 + 4 if you want to distinguish it from the original f(x) function