Charlie sells beaded bracelets as a side job. Charlie will have a maximum profit of $12 when he sells 5 bracelets. Construct Charlie’s profit function, p(x), to model his sales, in dollars, as a a function of the number of bracelets he sells.
p(x) = [a] (x-[h])^2 + [k]
Find [h]
responses
-12
12
-5
5
To find [h], we can use the given information that Charlie will have a maximum profit when he sells 5 bracelets. This means that the profit function will reach its maximum value when x = 5.
Given: p(5) = $12
So, we can plug in x = 5 into the profit function and set it equal to the maximum profit:
12 = [a] (5 - [h])^2 + [k]
Since the profit function reaches its maximum value when x = 5, we can solve for [h] by setting 5 - [h] = 0:
12 = [a] (0)^2 + [k]
12 = [k]
Now, we can plug in [k] = 12 into the equation:
12 = [a] (5 - [h])^2 + 12
0 = [a] (5 - [h])^2
So, [h] = 5.
Therefore, the correct response is:
h = 5