I don't typically begin teaching a new concept with an application, but this problem offers so many layers that it works really well.
Students split up into groups or pairs and determine the area of various rectangular houses based on a set perimeter and a given width. Already this requires some strategy and problem solving.
Then as a class, they collect and organize their data in a graph and a table. You can then use the graph to introduce new vocabulary (parabola, vertex, axis of symmetry,