Question

what is the y - value of the vertex of the function $f(x)=-(x - 3)(x + 11)$?
-8
-4
33
49

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$, solve $-(x-3)(x+11)=0$.
Roots are $x=3$ and $x=-11$.

Step2: Calculate vertex x-value

Vertex x is midpoint of roots:
$x=\frac{3 + (-11)}{2}=\frac{-8}{2}=-4$

Step3: Compute vertex y-value

Substitute $x=-4$ into $f(x)$:
$f(-4)=-(-4-3)(-4+11)=-(-7)(7)=-(-49)=49$

Answer:

49