Quadratic Word Problems

Question

Suppose that the equation p(x) = -2x^2+280x-1000, where x represents the number of items sold, describes the profit function for a certain business. How many items should be sold to maximize the profit?

Answer 1

p(x) = -2x^2+280x-1000

The maximum (or minimum) of a quadratic function occurs at x= -b/2/a where (x) = ax² + bx + c.

In this case, a = -2, b = 280, and c = -1000. Using the formula given, x = -280/2/(-2) = 70 items.