Answer:
[tex]\large\boxed{The\ vertex:\ (-5,\ 49)}[/tex]
Step-by-step explanation:
[tex]f(x)=ax^2+bx+c\\\\\text{The vertex}\ (h,\ k),\ \text{where}\ h=\dfrac{-b}{2a}\ \text{and}\ k=f(h).\\\\\text{We have:}\ y=-x^2-10x+24\to f(x)=-x^2-10x+24\\\\a=-1,\ b=-10,\ c=24.\\\\\text{Substitute:}\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)+24=-25+50+24=49[/tex]
