Question

what is the vertex of the quadratic function $f(x) = (x - 6)(x + 2)$?
(\boxed{},\boxed{})

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$, solve $(x-6)(x+2)=0$.
Roots: $x=6$ and $x=-2$

Step2: Calculate vertex x-coordinate

Average the intercepts: $x=\frac{6+(-2)}{2}$
$x=\frac{4}{2}=2$

Step3: Find vertex y-coordinate

Substitute $x=2$ into $f(x)$:
$f(2)=(2-6)(2+2)=(-4)(4)=-16$

Answer:

$(2, -16)$