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