def func(pseudo_state, a1, a2, b1, b2, c1, c2, d1, d2):
	"""
	quadratic fit function for the Bellman value at given pseudo-state
	
	:param pseudo_state: list(float) - list of the four state variables for a given state
	:param a1, a2, ... d2: float - parameters of the quadratic fit function
	"""
	sum = a1*pseudo_state[0]**2 + a2*pseudo_state[0]
	sum += b1*pseudo_state[1]**2 + b2*pseudo_state[1] 
	sum += c1*pseudo_state[2]**2 + c2*pseudo_state[2]  
	sum += d1*pseudo_state[3]**2 + d2*pseudo_state[3] 
	return sum