The graph of y = x^2 is shifted 4 units to the right. This graph is then vertically stretched by a factor of 5 and reflected across the x-axis. Finally, the graph is shifted 8 units upward.

y = x

^{2}To shift 4 units to the right, replace x with (x-4). (To shift left, replace x with (x+4))

y = (x-4)

^{2}To stretch vertically by a factor of 5, multiply (x-4) by 5

y = 5(x-4)

^{2}To reflect across the x-axis, change the sign of 5

y = -5(x-4)

^{2}To shift up by 8, simply add 8 to the expression:

y = -5(x-4)

^{2}+ 8Finally, multiply out the term -5(x-4)

^{2}and simplify to get the answer.