Answer
The axis of symmetry is $x=5$.
The vertex is $(5,4)$.
Work Step by Step
Comparing $f(x)=\frac{2}{5}x^{2}-4x+14$ with $f(x)=ax^{2}+bx+c$, we see that $a=\frac{2}{5}$ and $b=-4$.
Axis of symmetry is given by
$x=-\frac{b}{2a}=-\frac{-4}{2(\frac{2}{5})}=5$
The axis of symmetry is $x=5$.
As the axis of symmetry is $x=5$, the x-coordinate of the vertex is $5$.
We can use the function to find the y-coordinate.
$f(x)=\frac{2}{5}x^{2}-4x+14$
$f(5)=\frac{2}{5}(5)^{2}-4(5)+14=4$
The vertex is $(5,4)$.
