import numpy as np

def extremum(x, y):
    """
    Return extremum coordinates of quadratic fit
    """
    p = np.polyfit(x, y, 2)
    f = np.poly1d(p)
    if p[0] != 0:
        x_ext = -p[1] / (2 * p[0])
        y_ext = f(x_ext)
    else:
        x_ext = None
        y_ext = None
    yhat = f(x)
    ybar = np.sum(y)/len(y)
    ssreg = np.sum((yhat - ybar)**2)
    sstot = np.sum((y - ybar)**2)
    R2 = ssreg / sstot
    x_fit = np.linspace(min(x), max(x), 100)
    y_fit = f(x_fit)
    return (x_ext, y_ext, x_fit, y_fit, R2)