BRAINLIEST FOR CORRECT ANSWERRR The function f(x) = −x^2 + 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.

Part A:

The vertex :  x = - b / 2 a = - 28 : ( - 2 ) = 14

y = f ( 14 ) = - 14² + 28 · 14 - 192 = 196 + 392 - 192 = 4

The vertex is ( 14, 4 ). It means that the maximum hourly profit is $4, and that the shop should sell 14 sodas to reach the maximum.

Part B :

We will solve the quadratic equation:

x 1/2 = ( - 28 +/- sqrt ( 784 - 768 ) ) / ( - 2 )

x 1 = 12,  x 2 = 16.

It means that if the shop must sell more than 12 and less then 16 sodas if they want to make a profit ( 13, 14, or 15 ). If they sell 12, or 16 they will brake even. 

I think

answer: do we write it

step-by-step explanation: