let us consider g(x) = ax^2 +bx+c

from the graph we see that at x = 0 g(x)=-1

hence -1 = 0+0+C or c = -1

from the graph we see that at x = -1 g(x)=0

hence , 0 = a-b-1 or a-b = 1--------------(A)

from the graph we see that at x = 3 g(x)=-2

hence , -2 = 9a+3b-1 or 9a+3b = -1--------------(B)

solving A & B we get a = 1/6 & B = -5/6

hence g(x) = x^2/6 -5x/6 -1 (Answer)

THis answer also not fully correct ... some more information must be there to accurately trace the equation of the graph

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