The government of any such city operating under this chapter shall be known as the mayor-council form of government. Pursuant to the provisions and limitations of this chapter and subject to the limitations imposed by the Constitution and laws of Alabama, all powers of the city shall be vested in the council. The council is the sole authority to set the agenda for any of its meetings. All powers of the city shall be exercised in the manner prescribed by this chapter or, if the manner is not prescribed herein, in the manner prescribed by law or ordinance. A majority of the council members shall constitute a quorum for the transaction of any business of the council.