Finding the Vertex on the X-Axis

Consider the function defined by the equation:

$$ f(x) = 2x^2 - 8x + k $$

where $k$ is a constant. This function has its vertex at the point $(3, m)$, where $m$ is the $y$-coordinate of the vertex. Find the value of $m$ when $k$ is such that the parabola opens upwards and has its vertex on the $x$-axis.