This gives you three simultaneous equations:
6 = a + c
7 = 4a + c
1 = c
c = 1
If c =1,
6 = a + 1
a = 5
This doesn't work in the second equation, so the quadratic that goes through these points is not in the form y = ax^2 + bx + c
Was there supposed to be a b in the equation?