Indeed, notice that of the three given points, two points have equal y-coordinate,  (-1,6)  and  (3,6).


It means that these two points are symmetric relative to the vertical symmetry axis of the parabola.


It also means that vertical symmetry axis of this parabola has x-coordinate which is half of x-coordinates of the two points.


So, the equation of the symmetry axis is  x =  =  = 1.


After that, you notice that the third point (1,2) has x-coordinate 1, which means that this point (1,2) 
lies on the parabola's symmetry axis and, therefore, is the VERTEX of the parabola.


Having this info, we can write the vertex form equation of the parabola 

    y = a*(x-1)^2 + 2.


To determine the coefficient "a", substitute x= 3 into the equation for the point (3,6).  You will get


    6 = a*(3-1)^2 + 2

    6 - 2 = a*2^2

      4   = 4a

      a = 1.


Therefore, the parabola equation is


    y = (x-1)^2 + 2                       (the vertex form),  or


    y = x^2 - 2x + 1 + 2 = x^2 -2x + 3    (the general form)      ANSWER