### Home > CCA > Chapter 11 > Lesson 11.3.5 > Problem11-130

11-130.

The profit made by ACME Home Construction is represented by the function $y=−x^2+50x$ 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.

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