This page has a set of formulas for computing a bunch of common filter types: http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt
Those formulas also create A0 values, which can be normalized out like this:
A1 = A1/A0 A2 = A2/A0 B0 = B0/A0 B1 = B1/A0 B2 = B2/A0
Q is incorporated into the values computed by those formulas.
The main use case for entering these values manually is if you are building a digital crossover and know the names and parameters of the filters you’re after. IIR filters have a direct correspondence with analog crossover designs, so it is in principle possible to “port” an analog crossover into the digital domain very directly. Manual input of the values ensures that the design is translated properly without having to make assumptions about how our Parametric EQ works inside.
If you are just looking to adjust frequency response, the Parametric EQ can do the math for you.