Find the vertex, focus, and directrix of the parabola. 3x2 + 16y

i assume you mean 3x^2 + 16y = 0

so y = - 3/16 x^2

The vertex is at the origin (0,0) answer

x^2 = - 16/3 y

compare with standard form x^2 = 4ay:-

the focus y coordinate of the a = - 16/3 / 4

= - 16/12 = - 4/3 so the focus is (0, - 4/3) answer

and the directrix is y = 4/3 answer