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

Your maths is very weak try yourself this would improve your skills don't depend on others