Final answer:
The focus of a parabola with a vertex at (0,-2) and a directrix at x=4 is located at (-4,-2), four units away from the vertex in the opposite direction of the directrix along the x-axis.
Step-by-step explanation:
The student asked to identify the focus of a parabola with a vertex at (0,-2) and a directrix at x=4. To find the focus of the parabola, we need to use the vertex form of a parabola's equation and the fact that the vertex is equidistant from the focus and directrix.
The distance between the vertex and the directrix is 4 units (since the directrix is at x=4 and the vertex is at x=0). Therefore, the focus must be 4 units away from the vertex, but in the opposite direction along the x-axis, to maintain the equidistance property. Hence, the focus of the parabola will be at (-4,-2).