Answer questions about real world situation, given the quadratic functions that model them.

Problem

The profit, P, left parenthesis, x, right parenthesis, in millions of dollars, that a company makes from selling socks, is dependent on the price in dollars, x, that the socks are sold for. This relationship can be modeled with the function P, left parenthesis, x, right parenthesis, equals, minus, 3, left parenthesis, x, minus, 5, right parenthesis, start superscript, 2, end superscript, plus, 12.
What sock price should the company set to earn a maximum profit?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
dollars
What is the maximum profit that the company can earn?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
million dollars