Task 3 Quadratic Relationships

Length	Area of Rectangle
0	0
1	9
2	16
3	21
4	24
5	25
6	24
7	21
8	16
9	9
10	0

We can see this is not a linear relationship because the changes in areas are not constant. They increase to a certain area and then decrease by the same areas on the way back down. We can see the relationship is not exponential because the areas are not multiplied by the same number every time and they don't keep increasing or decreasing. The table goes up and then comes back down. We can also see if we take two differences those differences are constant. This is a characteristic of quadratic relationships.

The equation is Length x width. We have to write the equation for the area of the rectangle in terms of L. A= L(10-L). The graph is not a straight line that increases or decreases so it is not linear. The graph doesn't increase slowly and then increase fast, so it is not exponential. The graph is quadratic because of the u-shape or the arch. It has a maximum point and has a line of symmetry.