Answer:
Only option D is one of the transformations needed.
Step-by-step explanation:
The graph of f(x)=x^2 is a positive parabola with x=0 as the zero in ordinates and also 0 as a zero x. This is, the graph passes in (0,0) and this is the only point it crosses both axis, then for every x value we will gave a positive f(x).
Here I attach a graph that shows both, f(x)=x^2 and g(x)=-x^2+16x-44.
As you can see, for transforming f(x) in g(x) we need to reflect it over the x axis, as g is open downwards. Then, as the quadratic term is still being x^2 we do not wide it (as you see in the graph both curves are equally widened).
Then, we can also see that the graph is shifted right, so we do not shift it left 8 units (notice that we shift it right 8 units).
So, after reflecting over the x axis and shifting right we need to shift it UP, as we can see the graph is over the x axis.
So, the three transformations needed are:
1. reflect over the x axis
2. shift right 8 units
3. shift up 20 units.
So, from the options you proposed we chose only d, to which we MUST add the transformations noted above.
Sorry for the mistake!
