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.

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

Step-by-step 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.

dont think so

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet