### Instruction: Find the equation of the directrix of the parabola $y = 8x^2 + 2.$.### Response: I remember that the general form of a parabola with a vertical axis is $y = ax^2 + bx + c$, and the directrix is a horizontal line that is symmetric to the vertex and the focus of the parabola.
I also recall that the vertex of the parabola is the point $(h, k)$, where $h = -b/2a$ and $k = c - b^2/4a$.
In this problem, I can see that $a = 8$, $b = 0$, and $c = 2$, so the vertex is $(0, 2)$.
To find the focus, I use the formula $4a(p) = 1$, where $p$ is the distance from the vertex to the focus and the directrix.
Solving for $p$, I get $p = 1/32$.
Since the parabola opens upward, the focus is above the vertex, and the directrix is below the vertex.
Therefore, the focus has the coordinates $(0, 2 + 1/32)$, and the directrix has the equation $y = 2 - 1/32$.
This is the final answer.