Solution:
We are required to find the coordinates of the vertex for x^2+ 5x - 24 = 0
[tex]The\text{ x-coordinate of the vertex is x=}\frac{-b}{2a}[/tex][tex]\begin{gathered} For\text{ x}^2+5x-24=0 \\ a=1 \\ b=5 \\ x=-\frac{5}{2(1)} \\ x=-\frac{5}{2} \\ x=-2.5 \end{gathered}[/tex]To get the y coordinate, substitute x = -5/2 into the equation
[tex]\begin{gathered} \begin{equation*} \text{x}^2+5x-24=0 \end{equation*} \\ =(\frac{-5}{2})^2+5(\frac{-5}{2})-24 \\ \\ =\frac{25}{4}-\frac{25}{2}-\frac{24}{1} \\ =\frac{25-50-96}{4} \\ \\ =\frac{-121}{4} \\ \\ =-30.25 \end{gathered}[/tex]Hence, the coordinate of the vertex is (-2.5, -30.25)
