Question 367502
The x-coordinate of the vertex is {{{-b/(2a) = -2/(2*-2) = 1/2}}}.  The y-coordinate of the vertex is {{{-2(1/2)^2+2(1/2)+3 = -1/2+1+3 = 7/2}}}.  The line of symmetry is x = 1/2, and the maximum value is 7/2.