Type of filter represented by circuit and cutoff frequency
What type of filter does this circuit represent?


It's a 2nd order RLC high pass filter


  Also what would the cutoff frequency formula be in this case (of
  course that depends on what type of filter this is)?


Cutoff frequency = ~\$\dfrac{1}{2\pi\sqrt{LC}}\$

And no, if you have an L and a C forming a filter it's either high-pass, low-pass, band-pass or band-reject BUT in all cases the formula is the same i.e. a low pass 3 dB point is exactly same frequency as the high-pass 3 dB point. Notch and band-pass centre frequencies are identical too.

Low-pass example: -



High-pass example using the same values: -



Picture source.