Question

What are the coordinates of the vertex for x^2+ 5x - 24 = 0

Answer 1

We are required to find the coordinates of the vertex for x^2+ 5x - 24 = 0​

`The\text{ x-coordinate of the vertex is x=}(-b)/(2a)`
`\begin{gathered} For\text{ x}^2+5x-24=0 \\ a=1 \\ b=5 \\ x=-(5)/(2(1)) \\ x=-(5)/(2) \\ x=-2.5 \end{gathered}`

To get the y coordinate, substitute x = -5/2 into the equation

`\begin{gathered} \begin{equation*} \text{x}^2+5x-24=0 \end{equation*} \\ =((-5)/(2))^2+5((-5)/(2))-24 \\ \\ =(25)/(4)-(25)/(2)-(24)/(1) \\ =(25-50-96)/(4) \\ \\ =(-121)/(4) \\ \\ =-30.25 \end{gathered}`

Hence, the coordinate of the vertex is (-2.5, -30.25)