Question

What is the y-value of the vertex of the function f(x) = –(x – 3)(x + 11)?
The y-value of the vertex is

Answer 1

The y-value of the vertex is 49

Step-by-step explanation:

   Given, $f(x)=-(x-3)(x+11)$

$f(x)=-x^{2} -8x+33$

   The vertex of the parabola $y=ax^{2} +bx+c$ occurs at $x=\frac{-b}{2a}$.

For the given parabola, $a=-1,b=-8,c=33$

So, vertex occurs at $x=\frac{-(-8)}{2(-1)}=-4$

At this point $f(x)=-(-4-3)(-4+11)=7*7=49$

∴ At vertex, y-value of $f(x)=-(x-3)(x+11)$ is 49.