F(x)=X^(2)...Parabola is shifted 3 units to the left and 5 units up, then flipped upside down.

What is the formula for the parabola transformed into?

Take the transformation one step at a time.

To shift the parabola 3 units to the left, just replace x with x + 3 to get:
f(x) = (x + 3)^2.

Then, add 5 to shift the parabola up 5 units:
f(x) = (x + 3)^2 + 5.

To flip the parabola, just flip all of the signs to get:
f(x) = -(x + 3)^2 - 5.

I hope this helps!

g(x) = -(x + 3)² + 5

y = -(x+3)^2 - 5