Step-by-step explanation:
Given, [tex]f(x)=-(x-3)(x+11)[/tex]
[tex]f(x)=-x^{2} -8x+33[/tex]
The vertex of the parabola [tex]y=ax^{2} +bx+c[/tex] occurs at [tex]x=\frac{-b}{2a}[/tex].
For the given parabola, [tex]a=-1,b=-8,c=33[/tex]
So, vertex occurs at [tex]x=\frac{-(-8)}{2(-1)}=-4[/tex]
At this point [tex]f(x)=-(-4-3)(-4+11)=7*7=49[/tex]
∴ At vertex, y-value of [tex]f(x)=-(x-3)(x+11)[/tex] is 49.
