The graph of f(x) shown nelow in pink has the same shape as the graph of g(x)=x2 but it is flipped over the x axis and shifted down 2 units what is the equation

F(x) = -x^2 - 2

When applying changes to the parrent function of a quadratic ( x^2), a negative coefficient ( the negative in -x) will flip the parabola

adding/subtracting outside of the parenthesis will shift the parabola up/down
Parent function: x^2
Shifted 3 units up: x^2 + 3
Shifted 3 Units down: x^2 - 3

Adding/subtracting inside of the parenthesis will shift the parabola to the left/right
Parent function: x^2
Shifted to the left 4 units: (x + 4)^2
Shifted to the right 3 units: ( x - 3)^2
ATTENTION: When adding inside the parenthesis will cause the parabola to shift to the LEFT not to the right, subtracting will cause it to shift to the RIGHT