Answer
See below
Work Step by Step
Given: $y=x^2-5x-24$
We can see that $a=1\\b=-5\\c=-24$
Find the vertex: $x=-\frac{b}{2a}=-\frac{-5}{2(1)}=2.5\\y=-\frac{121}{4}=-30.25$
Find some points
$x=-3\rightarrow y=0\\x=0\rightarrow y=-24\\x=8 \rightarrow y=0$