[tex]\displaystyle\bf\\f(x)=-x^2+2x+4\\\\x_{max}=\frac{-b}{2a}=\frac{-2}{2\times(-1)}=\frac{-2}{-2}=\boxed{\bf1}\\\\y_{max}=\frac{-\Delta}{4a}=\frac{-(b^2-4ac)}{4a}=\frac{-(2^2-4\times(-1)\times4)}{4\times(-1)}=\\\\\\=\frac{-(4-(-16))}{-4}=\frac{-(4+16)}{-4}=\frac{-20}{-4}=\frac{20}{4}=\boxed{\bf5}\\\\\\\textbf{The maximum has the coordinates: }~~\boxed{\boxed{\bf~M(1,~5)~}}[/tex]
