Answer:
f(x) = -1/3x² -2x
Explanation:
For vertex (h, k) and scale factor "a", the vertex form of a quadratic is ...
y = a(x -h)² +k
For the given vertex, the vertex form function with scale factor "a" is ...
f(x) = a(x +3)² +3
If that goes through the point (-6, 0), then we have ...
f(-6) = a(-6 +3)² +3 = 0
9a = -3 . . . . . . . subtract 3
a = -1/3 . . . . . . . divide by 9
In standard form, the equation is ...
f(x) = (-1/3)x² -2x