If you plug these values in for x and y we obtain that the constants a, b and c must satisfy the system
4a-2b+c=0
a-b+c=1
a+b+c=3
From the second one we can see that c=1+b-a and if we substitute this into the last equation we obtain that a+b+1+b-a=3 or equivalently, 2b=2 or b=1. Hence, c=2-a which we substitute into the first equation of the system to get 4a-2+2-a=0. Thus, a=0 and x=2. So we do not have a parabola (since a=0) but a straight line given by y=x+2.
