`f(x)= - 4/7(x-6)^2+1`
We know that` (x-6)^2` is always positive or zero. Then `- 4/7(x-6)^2+1` is always negative or zero. So f(x) will have a maximum value. Maximum occurs when` - 4/7(x-6)^2` is maximum. Because of `-4/7` term the maximum that `- 4/7(x-6)^2` is 0. This comes when x = 6.
When x = 6 then f(x) = f(6) = 1.
So the vertex is (6,1).
As we described earlier f(x) will have a maximum. Graph is shown below.