The vertex form of [tex]f(x)=ax^2+bx+c[/tex]
[tex]f(x)=a(x-h)^2+k[/tex]
where: [tex]h=\dfrac{-b}{2a};\ k=f(h)[/tex]
We have: [tex]f(x)=-x^2-2x-3\to a=-1;\ b=-2;\ c=-3[/tex]
substitute:
[tex]h=\dfrac{-(-2)}{2\cdot(-1)}=\dfrac{2}{-2}=-1\\\\k=f(-1)=-(-1)^2-2\cdot(-1)-3=-1+2-3=-2[/tex]
The vertex form of f(x):
[tex]f(x)=-(x+1)^2-2[/tex]
