px² + qx + r =  p (x – h)² + k

                       = p(x² -2hx + h² ) + k

                       =px² -2phx + (ph² + k)

So comparing the coefficient of x,

q = -2ph   =>  h = -(q/2p)

Comparing the constant,

r = ph² + k     but we know  h = -(q/2p) from above,

So r = p[ -(q/2p) ]² + k

     r   = p [ (q² /4p² ) ] + k

Therefore,  k = r – (q² /4p)