This is vertex form of equation of a parabola. The general form of such a quadratic equation is #y=a(x-h)^2+k#.
As at #x=h#, we have #y=k#, the curve passes through #(h,k)#. This is called vertex, as it is at the tip of the curve.
If #a>0# than #a(x-h)^2# is positive and the minimum value of #y# will be #k# as the term #a(x-h)^2>=0#. In such cases curve opens up.
but if #a<0# than the term #a(x-h)^2# is negative and the maximum value of #y# will be #k# as the term #a(x-h)^2<=0#. In such cases curve opens down.
Further, #x=h# will be a line of symmetry, as value of #y# will always be same for any two values of #x# given by #x=h+-d#.
Here, the curve is given by #y=-2(x-4)^2+8#. Hence, we have #a=-2# and hence we have a maxima at #x=4#
and #x=4# is also axis of symmetry.
graph{-2(x-4)^2+8 [-7.12, 12.88, -1.4, 8.6]}
