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.

Question

p(x) = [a] (x-[h])^2 + [k]

Find [k]

responses

5
-5
12
-12

Answer 1

To find [k], we can substitute the values of x = 5 and p(x) = 12 into the profit function equation and then solve for [k].

12 = [a](5 - [h])^2 + [k]

Since Charlie's maximum profit of $12 is achieved when he sells 5 bracelets, the following equation holds true:

p(5) = 12

Substitute 5 for x in the function:

p(5) = [a](5 - [h])^2 + [k] = 12

Since the profit is maximized at 12, this can be simplified to:

[a](5 - [h])^2 + [k] = 12

Now we can solve for [k] using the value of x = 5:

[a](5 - [h])^2 + [k] = 12
[a](5 - [h])^2 + [k] = 12
[a](5 - [h])^2 = 12 - [k]
[a](5 - [h])^2 = 12 - [k]
[a](5 - [h])^2 = 12 - [k]
12 - [k] = 12
12 - [k] = 12
[k] = 12 - 12
[k] = 0

Therefore, the correct value of [k] is 0.