Let's examine the behavior of second order high pass transfer functions.
And compare that behavior to the behavior of
a first order high pass transfer function.
So I've written here both the first order, low pass and high pass transfer functions,
and the second order, low pass and high pass transfer functions.
Informing the second-order high-pass transfer function,
you can see that the denominator is exactly the same as it was for
the second-order low-pass transfer function.
But, the numerator is now equal to the highest order term, in the denominator.
Whereas for the low-pass filter,
the numerator was equal to the lowest order term in the denominator.
And similarly for the first order filters,
you form a first order high-pass filter by moving the highest ordered term in
the denominator to the numerator and you form a low-pass filter by
moving the lowest ordered term in the denominator to the numerator.