Math Reflection 1

1a. The graphs we've observed have parabolas that open down, and the tables we've observed have values that increase and decrease using the same numbers.
1b. The tables' values increase until it reaches the square of the middle number, and then it decreases back to the number it started with.

2. To find the maximum area for rectangles with a fixed perimeter using a graph, you go to the top of the parabola.
Using a table, you square the middle number.

3. Quadratic graphs have parabolas, while linear graphs have a straight line going at a constant rate and exponential graphs have a curve that's not a parabola.
Quadratic table values increase and decrease, while linear and exponential table values either increase or decrease.
Quadratic equations are modeled like: x(x+b)=y, and have an exponent that does not equal x and is a number larger than 2. Linear equations, on the other hand, are modeled like: y=mx+b, and do not have exponents at all. Finally, exponential equations have an exponent that equals x, and are modeled like: y=a(b)^x

-Sam and Diana