what is the vertex of the quadratic function $f(x)=(x - 6)(x + 2)$?

Explanation:

Step1: Expand the function

$f(x)=(x - 6)(x + 2)=x^{2}+2x-6x - 12=x^{2}-4x - 12$

Step2: Use the formula for the x - coordinate of the vertex

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex is $x=-\frac{b}{2a}$. Here, $a = 1$, $b=-4$, so $x=-\frac{-4}{2\times1}=2$.

Step3: Find the y - coordinate of the vertex

Substitute $x = 2$ into the function $f(x)=x^{2}-4x - 12$. Then $f(2)=2^{2}-4\times2 - 12=4-8 - 12=-16$.

Answer:

$(2,-16)$