A parabola has vertex $(4,2)$ and passes through $(2,0).$  Enter the equation of the parabola in the form "$y = ax^2 + bx + c$".
Since the parabola has vertex $(4,2),$ the equation of the parabola is of the form
\[y - 2 = k(x - 4)^2.\]Since the parabola passes through $(2,0),$ we can plug in $x = 2$ and $y = 0,$ to get
\[-2 = 4k,\]so $k = -\frac{1}{2}.$  Then
\[y - 2 = -\frac{1}{2} (x - 4)^2 = -\frac{1}{2} x^2 + 4x - 8,\]so the equation of the parabola is $\boxed{y = -\frac{1}{2} x^2 + 4x - 6}.$