The x-intercepts of the graph of y=P(x) represent the points where the profit (P) is equal to zero. In this case, the x-intercepts are x = 5 and x = 250, meaning the profit is zero when the company sells either 5 or 250 dresses.
Step-by-step explanation:
The x-intercepts of the graph of y=P(x) represent the points where the profit (P) is equal to zero. In this case, we have the equation
. Setting P(x) equal to zero, we can solve for x to find the x-intercepts.
To solve for x, set P(x) = 0:
From here, we can use the zero product property: when the product of two factors is equal to zero, at least one of the factors must be zero. So we have two cases to consider:
(x-5) = 0 or (x-250) = 0
Solving each equation, we find that the x-intercepts of the graph are x = 5 and x = 250. This means that the profit is equal to zero when the company sells either 5 or 250 dresses.
The probable question can be: A clothing company's profit for selling x dresses can be estimated with the equation P(x)=- 1/25 (x-5)(x-250) Interpret the x -intercepts of the graph of y=P(x) in the context of this problem.