According to one company’s profit model, the company has a profit of 0 when 10 units are sold and a maximum profit of $18,050 when 105 units are sold. What is the function that represents this company’s profit f(x) depending on the number of items sold, x?

A quadratic with a maximum of $18,050 at 105 units has vertex form f(x)=a(x−105)²+18,050, where a is negative. Since profit is 0 when 10 units are sold, substitute x=10: 0=a(10−105)²+18,050. Thus 9,025a=−18,050, so a=−2. Therefore the function is f(x)=−2(x−105)²+18,050, choice B.

AI-written and checked against the verified answer.