What is the vertex of the parabola, assuming p > 0? Is it (0, -p)?

To determine the vertex of the parabola, it's important to know the equation of the parabola and its orientation. However, assuming you are referring to a parabola that opens up or down and has its vertex on the y-axis, let's consider the standard form of the equation of a parabola that opens upward or downward:

\[ y = a(x-h)^2 + k \]

Here, \((h, k)\) is the vertex of the parabola, and the value of \(a\) determines whether the parabola opens upwards (if \(a > 0\)) or downwards (if \(a < 0\)). If the parabola is centered at the origin and \(p\) represents the distance from the vertex to the focus, the equation is typically written for an upward-opening parabola as:

\[ y = \frac{1}{4p}x^2 \]

Here, since the parabola is centered on the origin, the vertex is at the point \((h, k) = (0, 0)\). If the parabola opens downward, the equation is:

\[ y = -\frac{1}{4p}x^2 \]

Again, the vertex is at the point where \((h, k) = (0, 0)\), not \((0, -p)\). The value of \(-p\) might be referring to the directrix of the parabola, which is a line perpendicular to the axis of symmetry of the parabola and located a distance \(p\) from the vertex, but on the opposite side of the vertex from the focus.