Final answer:
The value of the constant l for the directrix of the given parabola y = 1/4x² - 2 is -2.25.
Step-by-step explanation:
The question is asking for the value of the constant l in the equation for the directrix of a parabola. The given parabola is in the form y = ax² + bx + c, which for this case is y = ⅛ x² - 2. To find the directrix of this parabola, we use the fact that for a parabola y = ax² + bx + c, the directrix is y = c - ⅝ / (4a) when the parabola opens upwards. In our equation, a = ⅛ and c = -2.
Following the formula for the directrix:
Directrix, y = -2 - (⅝ / (⅛ × 4))
= -2 - (1/4)
= -2 - 0.25
= -2.25
So, the value of the constant l for the directrix y = l is -2.25.