a) y = x^2-4
From the parent function, this graph is translated vertically by -4 units, or moved down 4 units.
b) y = -(x+1)^2+3
This graph is reflected across the x axis, so there would be a negative outside of the x. It is also translated horizontally by -1 unit. When a graph is moved to the left, the x gets added to. When it is moved to the right, the x gets subtracted from. Since the graph is translated left by 1 unit, there would be a +1 attached to the x. Parenthesis is important here. The graph is also translated up 3 units, so you add 3 at the end.