### Home > CCA > Chapter 11 > Lesson 11.3.5 > Problem 11-130

11-130.

The profit made by ACME Home Construction is represented by the function *y* = −*x*^{2} + 50*x* where *x* = the number of homes built and *y* = the profit in thousands of dollars. How many homes should be built to maximize the profit? Hint: Think about the graph of the function. *11-130 HW eTool** *(Desmos). Homework Help ✎

Start by converting the equation to graphing form by completing the square.

Does this parabola open up or down?

Where is the vertex?

Does the vertex represent the maximum *y*-value?

25 houses

Use the eTool below to graph the function.

Click the link to the right for full version. CCA 11-130 HW eTool