Answer
The axis of symmetry is $x=1$.
The vertex is $(1,-2)$.
Work Step by Step
Comparing $f(x)=2x^{2}-4x$ with $f(x)=ax^{2}+bx+c$, we see that $a=2$ and $b=-4$.
Axis of symmetry is given by
$x=-\frac{b}{2a}=-\frac{-4}{2(2)}=1$
The axis of symmetry is $x=1$.
As the axis of symmetry is $x=1$, the x-coordinate of the vertex is $1$.
We can use the function to find the y-coordinate.
$f(x)=2x^{2}-4x$
$f(1)=2(1)^{2}-4(1)=-2$
The vertex is $(1,-2)$.
