The students will construct several rectangles with different dimensions, all having the same perimeter. The area of each rectangle is then computed and plotted against the width of each rectangle. The students will discover that the area is a quadratic function of the width. They will also discover that the rectangles attain a maximum area.

Each student will be assigned with two numbers from the set {.5, 1, 1.5, 2, 2.5, . . . . 19.5}. They also need to log into the TI-Navigator.

Discuss first difference in x and second difference in y. Let the students use the calculator and quadratic regression to find the function. Also, let the students discover the maximum area from the table and confirm this by finding the value of the vertex in the calculator. Discuss also the attributes of square and rectangles.

In this activity,the students will deepen their understanding about domain, range, quadratic function and maximum value of a function.

Discuss the the proof and let the students write their arguments regarding squares and rectangles.