Question

A home-based sign company uses this function to model its monthly profit, where x is the price of each sign it sells. p(x) = -10x² + 498x - 1,500. What is the function used to model the monthly profit of the sign company?

1) -10x² + 498x - 1,500
2) -10x² + 498x
3) 498x - 1,500
4) -10x²

Answer 1

The function for the sign company's monthly profit is -10x² + 498x - 1,500, a quadratic function that shows the relationship between the price of signs and profit.

Step-by-step explanation:

The function used to model the monthly profit of the home-based sign company is -10x² + 498x - 1,500. This is a quadratic function where x represents the price of each sign sold, and p(x) represents the monthly profit. In this function, the term -10x² causes the graph to open downwards (as it is a negative quadratic), indicating that there will be a maximum profit at a certain price point. The 498x term shows a linear relationship between price and profit up to that point, and the constant term of -1,500 represents the initial costs or losses when no signs are sold.