Answer:
49.
Step-by-step explanation:
We have been a function [tex]f(x)=-(x-3)(x+11)[/tex]. We are asked to find the y-value of vertex of the given function.
Upon multiplying both factors, we will get,
[tex]f(x)=-(x*x+11*x-3*x-3*11)[/tex]
[tex]f(x)=-(x^2+11x-3x-33)[/tex]
[tex]f(x)=-(x^2+8x-33)[/tex]
[tex]f(x)=-x^2-8x+33[/tex]
Now, we will use [tex]\frac{-b}{2a}[/tex] formula to find the x-coordinate of vertex of parabola.
[tex]\frac{--8}{2*-1}[/tex]
[tex]\frac{8}{-2}[/tex]
[tex]-4[/tex]
Since the x-coordinate of vertex of parabola is [tex]-4[/tex], so we will substitute [tex]x=-4[/tex] in our equation to find y-coordinate of parabola.
[tex]f(-4)=-(-4)^2-8(-4)+33[/tex]
[tex]f(-4)=-16+32+33[/tex]
[tex]f(-4)=49[/tex]
Therefore, the y-coordinate of vertex of the given parabola is 49.
