-51
First, find the axis of symmetry, or the x value where the line switches directions. This is also the x value of the vertex. Find this by using the equation -b/2a. In this case, -10 is b, and 1 is a.
-(-10)/2(1)
10/2
5
So, the x value of the vertex is 5. Now, find the y value by putting the x value back into the equation.
y = -(5)^2 - 10(5) + 24
y = -25 - 50 + 24
y = -75 + 24
y = -51
So, the y value of the vertex is -51.
