A new restaurant in Orlando Florida determined to maximize profits for the evening,they need to seat 30 tables of guests. One evening, they were only able to serve 16 tables, earning a profit of $352 for the day. The restaurant is attempting to turn a maximum profit of $450 for the day. The relationship between the restaurants profit, y, and the number of tables served, x, can be modeled by a quadratic equation.

Find the value of a for the quadratic equation modeling the restaurants profit.