Final answer:
To find the vertex of the parabola x² = -24y, recognize that it is a downward-opening parabola with its vertex on the axis of symmetry, the y-axis. Given the lack of a linear or constant term in the equation, the vertex is at the origin, (0, 0).
Step-by-step explanation:
The question asks to find the vertex of the parabola represented by the equation x2 = -24y. The general form of a parabola's equation when it opens upward or downward is y = ax2 + bx + c. Since the given equation can be rewritten as y = -1/24 x2, the parabola opens downwards and the coefficient of x (the 'b' term) is 0. This means the vertex occurs at the axis of symmetry of the parabola which is the y-axis in this case, so we know the x-coordinate of the vertex is 0. As the parabola is symmetrical around the y-axis and given that there is no constant term (the 'c' term) in the equation, the y-coordinate of the vertex is also 0. Thus, the coordinate of the vertex is (0, 0).