Displaying the graph of an EQ curve

Just like this guy: STM32F4 Audio DSP Demo - part 2 - Graphics - YouTube

Any ideas? I can't even work out how to make a math function for the curve of a lets say +4dB high shelf filter...

There are literally thousands of books on the subject. Start simple. For example, a single-pole low pass filter:

H(w) = 1 / (j(w/wc) + 1)

As the comment on the video states, the filter is a biquad in various configurations.