If a function, f(x) is translated c units to the left, it becomes f(x + c).
The given function is
f(x) = x^2
If we translate it 5 units to the left, it becomes (x + 5)^2
Also,
If a function, f(x) is translated d units upwards, it becomes f(x) - d
If we translate (x + 5)^2 upwards by 3 units, the function rule becomes
g(x) = (x + 5)^2 + 3
