Question

determine the quadratic function whose graph contains the points(-2,-1), (-1,0), and (-3,0).

Answer 1

Assume the quadratic function is of the form
y(x) = ax^2 + bx + c

The three points give you three equations in the three unknowns.
-1 = 4a -2b +c
0 = a -b +c
0 = 9a -3b +c

Subtract the second from the first and the second from the third to get two independent equations without x.

-1 = 3a -b
0 = 8a -2b

-2 = 6a -2b
2a = 2
a = 1 b = 4 c = b-a = 3

y = (x^2 + 4x +3) = (x+1)(x+3)

Answer 2

I meant to write "Subtract the second from the first and the second from the third to get two independent equations without c"

One could also write one equation for a circle that passes through those three points, but it would contain a y^2 term as well as the x^2, x and constant terms