We are starting with the parent function \(f(x) = x^2\)

STEP 1: Vertically compress the graph by a factor of 1/2, to get \(y=(1/2)x^2\)

STEP 2: Shift the graph by 1 unit to the right, to get \(y=1/2(x-1)^2\)

STEP 3: Shift the graph by 2 units downwards, to get \(y=1/2(x-1)^2)-2\), which is the required function h(x)