Rabbit Run

Learning Focus

Model area with a fixed perimeter and identify vertex / maximum features of a quadratic.

Big idea

With 72 ft of fencing for a rectangle, if one side is $x$, the adjacent side is $36-x$ (because $2x+2w=72$).

Area: $A(x)=x(36-x)=36x-x^2$.

Maximum area occurs at the vertex of this downward parabola.

Takeaways

• Not all quadratics are discrete figure patterns — some are continuous area models.
• Vertex form / symmetry helps find max/min.