You can put this solution on YOUR website!
the max/min of a parabola is the vertex , which is on the axis of symmetry
general equation for the axis of symmetry ___ x = -b / (2a)
in this case ___ x = (-2) / (2 * (-1)) = (-2) / (-2) = 1
plug into the function to find the vertex ___ g(x) = -(1)^2 + 2(1) + 8 = 9 ___ the vertex is (1,9)
the coefficient of the squared term is negative , so the parabola opens downward
this means that the vertex is an absolute maximum