The profit p, in dollars, of a small business can be modeled by the function p(x) =...
Check the final answer first, then review the worked steps.
Problem
The profit p, in dollars, of a small business can be modeled by the function p(x) = 2x^2 - 3x - 3, where x is the number of units sold. How many units need to be sold for the business to make a profit of $6?
Step-by-step solution
Set the profit function equal to $6 and solve the quadratic equation $2x^2 - 3x - 3 = 6$ for $x$. This simplifies to $2x^2 - 3x - 9 = 0$. Factoring or using the quadratic formula yields $x = 3$ and $x = -1.5$. Since the number of units sold cannot be negative, we take the positive value.
Answer
3, -1.5