I have fit a second order polynomial to a number of x/y points in the following way:

poly  = np.polyfit(x, y, 2)

How can I invert this function in python, to get the two x-values corresponding to a specific y-value?

Here's an example that shows how you can combine your poly with my answer at Inverse function of numpy.polyval().

First some data:

In [44]: x
Out[44]: array([0, 1, 2, 3, 4, 5, 6, 7])In [45]: y
Out[45]: array([ 9,  4,  0, -1, -1,  4,  8, 16])

Fit a polynomial to the data:

In [46]: poly = np.polyfit(x, y, 2)

Find where the polynomial has the value y0

In [47]: y0 = 4

To do that, create a poly1d object:

In [48]: p = np.poly1d(poly)

And find the roots of p - y0:

In [49]: (p - y0).roots
Out[49]: array([ 5.21787721,  0.90644711])

Check:

In [54]: x0 = (p - y0).rootsIn [55]: p(x0)
Out[55]: array([ 4.,  4.])