Question

What is the vertex of the quadratic function f(x)=(x-8)(x-2)?

Answer 1

change the function into vertex form:
f(x)=x²-10x+16
make a square by (adding half of -10)², which is 25, then subtract it:
f(x)=x²-10x+25-25+16
f(x)=(x-5)²-9
so the vertex is at (5,-9)

another way to do it: 
f(x)=x²-10x+16
the vertex is when x=-$\frac{b}{2a}$, b=-10, a=1 in this case.
x=-(-10/2*1)=5
plug x=5 into the quadratic function, you get f(x)=-9