When combining translations and reflections the order in which you do them is important.
A general rule for drawing the transformations:
First - Apply Reflections
Second - Apply Translations
#1
On one axis graph y=x2
On the same axis graph y=-x2+3 in a different color
(Just in case the transformations are an x-axis reflection and a vertical shift up)
#2
Copy this graph onto an axis call it f(x)
On the same axis graph -f(x+1) in a different color
(Just in case the transformations are an x-axis reflection and a horizontal shift left)
#3
Copy this graph onto an axis call it g(x)
On the same axis graph g(-x)+2 in a different color
(Just in case the transformations are a y-axis reflection and a vertical shift up)