The profits of a company from 1996 to 2005 can be modeled by P = 20t 2 + 80t + 20000 where t is the number of years since 1996. What is the company’s minimum profit? *Hint: Convert to vertex form.

Answer 1

To get minimum let change to vertex form: P(t) = 20(t + 2)² - 800 + 20000; P(t) = 20(t + 2)² + 19200.

From here we see that minimum will be at t = 0 (because this model working for t ≥ 0).

P_min = $20000