Answer:
(a, b, c) = (1, -4, 3)
Step-by-step explanation:
In vertex form, the equation is ...
... f(x) = a(x -2)² -1
This has a y-intercept of ...
... f(0) = a(0 -2)² -1 = 4a -1
We want that value to be 3, so we can find "a" as ...
... 4a -1 = 3 . . . . . set f(0) = 3
... 4a = 4 . . . . . . . add 1
... a = 1 . . . . . . . . divide by 4
Then ...
... f(x) = (x -2)² -1 = x² -4x +3
The coefficients are a=1, b=-4, c=3.
