Move a parabola

Moving $y = x^2$ gives $y = a(x - h)^2 + k$. You will find a vertex from the standard form, turn the vertex form back into the standard form, and find the zeros.

The idea. The vertex of $ax^2 + bx + c$ is at $x = -\dfrac{b}{2a}$. Expanding $a(x - h)^2 + k$ gives $a$, $-2ah$ and $ah^2 + k$.

Your tasks.

1. In vertex, return the vertex (x, y) of $ax^2 + bx + c$.
2. In standard, return (a, b, c) for $a(x - h)^2 + k$.
3. In zeros, return the sorted list of real zeros, or an empty list.