Given that the quadratic equation is ![y=-x^{2}-10 x+24](https://tex.z-dn.net/?f=y%3D-x%5E%7B2%7D-10%20x%2B24)
We need to determine the y - value of the vertex.
<u>The x - value of the vertex:</u>
The x - value of the vertex can be determined using the formula,
![x=-\frac{b}{2 a}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7Bb%7D%7B2%20a%7D)
where ![a=-1, b=-10, c=24](https://tex.z-dn.net/?f=a%3D-1%2C%20b%3D-10%2C%20c%3D24)
Substituting these values, we get;
![x=-\frac{(-10)}{2(-1)}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B%28-10%29%7D%7B2%28-1%29%7D)
Simplifying the terms, we get;
![x=-\frac{-10}{-2}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B-10%7D%7B-2%7D)
![x=-5](https://tex.z-dn.net/?f=x%3D-5)
Thus, the x - value of the vertex is -5.
<u>The y - value of the vertex:</u>
The y - value of the vertex can be determined by substituting the x - value of the vertex ( x = -5) in the equation ![y=-x^{2}-10 x+24](https://tex.z-dn.net/?f=y%3D-x%5E%7B2%7D-10%20x%2B24)
Thus, we get;
![y=-(-5)^{2}-10(-5)+24](https://tex.z-dn.net/?f=y%3D-%28-5%29%5E%7B2%7D-10%28-5%29%2B24)
Simplifying the values, we have;
![y=-25+50+24](https://tex.z-dn.net/?f=y%3D-25%2B50%2B24)
![y=49](https://tex.z-dn.net/?f=y%3D49)
Thus, the y - value of the vertex is 49.