Given that the quadratic equation is [tex]y=-x^{2}-10 x+24[/tex]
We need to determine the y - value of the vertex.
The x - value of the vertex:
The x - value of the vertex can be determined using the formula,
[tex]x=-\frac{b}{2 a}[/tex]
where [tex]a=-1, b=-10, c=24[/tex]
Substituting these values, we get;
[tex]x=-\frac{(-10)}{2(-1)}[/tex]
Simplifying the terms, we get;
[tex]x=-\frac{-10}{-2}[/tex]
[tex]x=-5[/tex]
Thus, the x - value of the vertex is -5.
The y - value of the vertex:
The y - value of the vertex can be determined by substituting the x - value of the vertex ( x = -5) in the equation [tex]y=-x^{2}-10 x+24[/tex]
Thus, we get;
[tex]y=-(-5)^{2}-10(-5)+24[/tex]
Simplifying the values, we have;
[tex]y=-25+50+24[/tex]
[tex]y=49[/tex]
Thus, the y - value of the vertex is 49.
