Be just a bit clearer, please: "find the vertex."
You could either "complete the square" or use the "quadratic formula."
Here the coefficients are a=-1, b=11 and c=-18. Because a is -, the curve opens downward and the vertex is on top, representing the function's maximum.
Use the quadratic formula with the coefficients given above.
-b plus or minus sqrt(b^2-4ac)
x = -------------------------------------------
2a