Final answer:
The value of the directrix l for the parabola y = 1/12x^2 - 6 is -9.
Step-by-step explanation:
The student is asking for the value of l, which represents the directrix of the parabola given by the equation y = 1/12x^2 - 6. In the context of this equation, the directrix is a horizontal line, and its equation will be of the form y = l. To determine this value, one must understand the properties of a parabola. For the parabola y = ax^2 + bx + c, the vertex form is expressed as y = a(x - h)^2 + k, where the vertex is at the point (h, k) and the directrix is y = k - 1/(4a) if the parabola opens upwards or downwards. The given equation is already in the form y = ax^2 + c; hence it's simplified, without a linear term, indicating that the vertex lies on the y-axis. Since the coefficient a = 1/12, and there is no h because the vertex lies on the y-axis, computing the directrix only requires finding the value of k from the equation y = ax^2 + k. The given equation lacks an explicit k value, but since the parabola is shifted 6 units down, we take k = -6. Therefore, l, the value of the directrix, can be calculated using the formula k - 1/(4a), resulting in l = -6 - 1/(4*(1/12)), which after simplification leads to l = -6 - 3 or l = -9.