For integers "a" and "T, \(T \neq 0,\)" a parabola whose general equation is "y=ax^2+bx+c" passes through the points "A=(0,0),B=(2T,0), and C=(2T+1, 28)". Let "N" be the sum of the coordinates of the vertex point. Determine the largest value of "N".
The answer is -47.