algebra precalculus - How-To Quadratic Funcions and Graphs

I have the following problem: For $f(x) = −x^2 + 4x − 8$ the value of $-b\over{2a}$
is $2$. Find the $y$-coordinate of the vertex of the graph of this function.

My book is severely lacking in material for the solution to this answer. I believe that to solve this we need to set our function to $y$ with a value of $2$, then solve.

If you could tell me which strategy to use or provide an explanation with a solved equation I would appreciate it.

Answer

The coordinates of the vertex are $(\dfrac{-b}{2a}, f(\dfrac{-b}{2a}))$.

In that specific case, the $y$-coordinate is $f(2) = -2^2 + 4 \cdot 2 -8 = -4$.