Question

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.

A- (12, 16); The vertex represents the maximum profit.

B- (12, 16); The vertex represents the minimum profit.

C- (14, 4); The vertex represents the maximum profit.

D- (14, 4); The vertex represents the minimum profit.

Answer 1

9514 1404 393

Answer:

C- (14, 4); The vertex represents the maximum profit.

Explanation:

The leading coefficient of the quadratic function is negative, so the graph opens downward, and the vertex represents a maximum.

The maximum value is at ...

x = -b/(2a) = -28/(2(-1)) = 14

f(14) = -14^2 +28(14) -192 = 4

The vertex is (14, 4). It represents the maximum profit.