The function, f, shifts the parent function 5 units

To shift right 5 units equation needs to be: y=0.5(x-5)^2

To shift left 5 units equations needs to be y=0.5(x+5)^2

To shift up 5 units equation need to be y=0.5x^2 +5

To shift down 5 units equation need to be y=0.5x^2 -5

For the question with 8 units just replace all the 5 with 8.