3)
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 function of the number of bracelets he sells.
p(x)= [a](x−[h])2+[k]
Find [a]
(1 point)
Responses
−34
negative 3 fourths
34
To find the value of `[a]`, we can use the information given in the problem:
When Charlie sells 5 bracelets, he makes a maximum profit of $12. This means that the point (5, 12) lies on the graph of the profit function `p(x)`.
Substitute the point (5, 12) into the standard form of the profit function to find `[a]`:
12 = [a](5 - [h])^2 + [k]
Since we know that `(5, 12)` is a maximum point, `h` will be the x-coordinate of the maximum point. Since the maximum point is (5, 12), h = 5:
12 = [a](5 - 5)^2 + [k]
12 = [a](0)^2 + [k]
12 = [k]
12 = [a](0) + 12
12 = 0 + 12
12 = 12a
a = 1
So, `[a] = 1`