Final answer:
The function g(x) involves horizontal scaling by a factor of 2, a horizontal shift to the left by 3 units, a vertical reflection, and a downward vertical shift by 5 units.
Step-by-step explanation:
The transformation of the parent graph f(x) = x² represented by the function g(x) = -(2x+3)² - 5 includes several steps. First, the function is horizontally scaled by a factor of 2, due to the 2x inside the parenthesis. Next, it is horizontally shifted 3 units to the left, as indicated by the +3. The negative sign outside the squared term reflects the graph vertically over the x-axis. Finally, the graph is vertically shifted downwards by 5 units, represented by the -5 at the end of the function. These transformations significantly alter the shape and position of the parabola represented by the original parent function.