Question

shifting functions vertically and horizontally

Answer 1

Shifted left by 4, so (x+4)^2.
Shifted down by 2, so (x+4)^2 -2 .

Answer 2

The red graph has been shifted four units to the left and two units down to obtain the blue one.

As such its equation becomes f(x + 4) - 2

Since f(x) = x^2
So f(x + 4) - 2 = (x + 4)^2 - 2