Students are presented with a classic optimization problem of a rectangle with two vertices on the x-axis and two vertices on a parabola. They will explore the concept of maximum area of the rectangle graphically, numerically, and algebraically.
Before the Activity
This investigation could be used as an introduction to optimization (max-min) problems in precalculus or calculus. Students should be familiar with polynomial functions. They should also be able to represent coordinates in terms of functions.
During the Activity
This activity is intended to be student-centered with the teacher acting as a facilitator while students work cooperatively. Students will answer the questions posed on the Q&A Notes pages.