[tex]y=-x^2+4x-5\\\\a=-1, \ b=4, \ c=-5\\\\\Delta=b^2-4ac\rightarrow 4^2-4\cdot1\cdot(-5)=16-20=-4\\\\p=\frac{-b}{2a}=\frac{-4}{2\cdot(-1)}=\frac{-4}{-2}=2\\\\q=\frac{-\Delta}{4a}=\frac{-(-4)}{4\cdot(-1)}=\frac{4}{-4}=-1\\\\y=a(x-p)^2+q\\\\\huge\boxed{y=-(x-2)^2-1}[/tex]