Because A(2, -2)B(3, -2)C(- 1, 10) passes through a parabola, three points of it are respectively substituted into the parabolic analytical formula.

2^a*2+2b+c=-2

3^a*2+3b+c=-2

(- 1)^a*2-b+c= 10

The solutions are a = 1, b =-5 and c = 4.

So the analytical formula of this parabola is y = a-5x+4.