def calc_parabola_vertex(points):
    """Adapted and modifed to get the unknowns for defining a parabola

    Parameters
    ----------
    points : list
        Three points on the pump characteristics curve.
    """
    [(x1, y1), (x2, y2), (x3, y3)] = points
    denom = (x1 - x2) * (x1 - x3) * (x2 - x3)
    A = (x3 * (y2 - y1) + x2 * (y1 - y3) + x1 * (y3 - y2)) / denom
    B = (x3 * x3 * (y1 - y2) + x2 * x2 * (y3 - y1) + x1 * x1 * (y2 - y3)
        ) / denom
    C = (x2 * x3 * (x2 - x3) * y1 + x3 * x1 * (x3 - x1) * y2 + x1 * x2 * (
        x1 - x2) * y3) / denom
    return A, B, C
