The function f(x) = −x2 + 28x − 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number of sodas sold.

Determine the vertex, and explain what it means in the context of the problem.

(12, 16); The vertex represents the maximum profit.
(12, 16); The vertex represents the minimum profit.
(14, 4); The vertex represents the maximum profit.
(14, 4); The vertex represents the minimum profit.