def _idealized_arc_curve(n, x):
    """
    Returns the value at x for the parabola of width n and height n / 2.
    Formula taken from https://www.desmos.com/calculator/awtnrxh6rk.

    Parameters
    ----------
    n: Length of the time series to calculate the parabola for.
    x: location to compute the parabola value at.
    """
    height = n / 2
    width = n
    c = width / 2
    b = height
    a = height / (width / 2) ** 2
    y = -(a * (x - c) ** 2) + b
    return y