I'll start with the vertex (3,1) fromula for a parabola
y = a (x-h)^2 + k
y = a ( x-3)^2 + 1 now pick a convenient point on the graph .... how about 0,7 sub in to calcualate a
7 = a ( -3)^2 + 1 shows a = 2/3
y = 2/3 (x-3)^2 + 1 expand
y = 2/3 x^2 -4x + 7 <===== finish from here