Question

The function f(x)=x^2 has been translated 9 units up and 4 units to the right to from the function g(x) which represents

Answer 1

For translations like this use the formula:
f(x) = (x - h)² + k

where h is the lateral movement/shifts on the x-axis and k is the vertical movement/shifts on the y-axis.

Since g(x) is a movement to the right 4 units and up 9 units, your h is a positive 4 and k is a 9:

g(x) = (x - 4)² + 9

Here's a picture of your original graph f(x) and your translation g(x)