Which describes how to graph h(x)= -3 squared root x+8 by transforming the parent function?

The parent function is f(x) = ∛x

When you change the sign to get g(x) = - ∛x you are reflecting the function over the x-axis (because you are changing the sign of all the images).

When you do g(x + 8) to get h(x) = - ∛ (x + 8) you are shifting the functions 8 units to the left.

Therefore, the answer is the fourth option: reflect the parent function over the x-axis and translate it 8 units to the left.