Answer
vertex: $(4,2)$
Focus: $(4,\frac{19}{8})$
Directrix: $y=\frac{13}{8}$
Work Step by Step
$2x^2-16x-3y+38=0$
$(x-4)^2=\frac{3}{2}(y-2)$
Thus,
vertex: $(4,2)$
Focus: $(4,\frac{19}{8})$
Directrix: $y=\frac{13}{8}$