Question 353026
Here, {{{a=1}}}, {{{b=12}}}, {{{c=1}}}.
The x-coordinate of the vertex is {{{-b/2a}}}.  The y-coordinate of the vertex is {{{(4*a*c-b^2)/(4a)}}}.
{{{-b/2a=-12/(2*1)=-6}}}.  
{{{(4*a*c-b^2)/(4a)=(4*1*1-144)/(4*1)=-35}}}.
The axis of symmetry is the vertical line {{{x=-6}}}.
There is no max value.  (The parabola opens upward.)
The minimum value is {{{y = -35}}}.