Answer:
49
Step-by-step explanation:
The given function is [tex]f(x)=-(x-3)(x+11)[/tex].
We expand to get:
[tex]f(x)=-x^2-8x+33[/tex]
We complete the square to obtain the vertex form as follows:
[tex]f(x)=-(x^2+8x)+33[/tex]
[tex]f(x)=-(x^2+8x+16)--16+33[/tex]
[tex]f(x)=-(x^2+8x+16)+16+33[/tex]
[tex]f(x)=-(x+4)^2+49[/tex]
This function is now of the form:
[tex]f(x)=a(x-h)+k[/tex], where (h,k)=(-4,49) is the vertex.
The y-value of the vertex is therefore 49
