The parent function is

\(f(x)=x^2\)

To find the new function g (x):

Applying Horizontal shift 23 units to the right as shown below,

\(f(x)=(x-23)^2\)

Applying vertical shift 52 units to the up as shown below,

\(f(x)= 52+(x-23)^2\)

Therefore, the parent function f(x)is transformed to another function.

\(g(x)=52+(x-23)^2\)

\(f(x)=x^2\)

To find the new function g (x):

Applying Horizontal shift 23 units to the right as shown below,

\(f(x)=(x-23)^2\)

Applying vertical shift 52 units to the up as shown below,

\(f(x)= 52+(x-23)^2\)

Therefore, the parent function f(x)is transformed to another function.

\(g(x)=52+(x-23)^2\)