How can the graph of f (x) = 1/2 (x+3) ^2 - 3 be obtained from the graph of y=x^2

Shift the graph 3 units to the left, add 3 to x.

Compress graph vertically by a factor of 2, multiply by 1/2, (or divide by two : P)

Shift graph downwards by 3 units, subtract a constant of 3 from the equation.