Answer:
f(x) = - (x - 5)² - 5
Step-by-step explanation:
The vertex form of the quadratic function is:

Given that it has a vertex at (5, -5),
(h,k)=(5,-5)

Since it passes through the point (7,-9)
When x=7, f(x)=-9

Therefore, the function is:
f(x) = - (x - 5)² - 5