I have a question on my math problem.

Question

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]

I need help finding a, h, and k

Answer 1

The problem assumes a parabolic function

then the vertex or maximum point or profit is (5,12) = (h,k) h= 5, k=12

Off hand, the value of a eludes me, as I suspect you need more information to calculate a

My guess is a=-1 probably works as well as any value. Since this is maximum profit, the parabola is

downward opening and a<0

so

P(x) = -(x-5)^2 + 12

you have -k on the right, it's usually +k. as the parabola equation in vertex form

standard form is y-k= a(x-h)^2

But if you didn't have a typo and really want -k then change the sign and make k=-12