Math Reflection

1.a. Graphs and tables of quadratic functions both escalate to a maximum and then decrease symmetrically. The greatest area of a rectangle with a fixed perimeter occurs when the length and width are the same, which appears on the graph as the quadratic function's maximum. A quadratic functions graph also has two x-intercepts.
1.b. In a quadratic function, both the tables and graphs escalate to a maximum and then decrease symmetrically. When x is the length of a rectangle and y is the rectangle's area, and the rectangle has a fixed perimeter, the maximum is the rectangle when the rectangle's length and width are the same. This is an example of a quadratic function.
2. One way to find the maximum area for rectangles with a fixed perimeter is to find the highest point on the parabola representing the quadratic function on a graph. You can also find the maximum area with a table. The greatest area is when the length and width are the same.
3. Tables, graphs, and equations of quadratic functions do not increase or decrease at a steady rate like those for linear functions, nor do they curve exactly like exponential functions. Graphs of quadratic functions always show a parabola, which is unique to quadratic functions.

by Noah S., Peter S., and Ryan F.