Force minimum of quadratic fit to certain data point

Question

I want to fit some data $(x_i, y_i)$ with quadratic function. No problem till there. However, I want the polynomium minimum of the fitted curve to be at certain point $(x_k, y_k)$. If it is possible, I'd like a python example.

Here is the data I work with:

In [161]: x
Out[161]: 
array([ 0. ,  0.1,  0.2,  0.3,  0.4,  0.5,  0.6,  0.7,  0.8,  0.9,  1. ,
        1.1])

In [162]: y
Out[162]: 
array([-78314.37119, -78314.4009 , -78314.40665, -78314.40274,
       -78314.39626, -78314.39821, -78314.39658, -78314.38418,
       -78314.37636, -78314.35708, -78314.33658, -78314.29853])

In [159]: xf
Out[159]: [0.2]

In [160]: yf
Out[160]: [-78314.40665]

xf and yf are the coordinates of the quadratic fitted minimum (which is the minimum of all the (x,y) values)