1.2+Reading+a+Graph

24/01/09 AE Notes: A parabola is a graph that is shaped like a mountain that peaks up, then returns down again.

__1.2 Reading a Graph__

//A) The graph goes up and then it has a peak, then it returns down again. This is called a Parabola.//
 * A) Describe the shape of the graph and any special features you observe**.

//B)// //The greatest area possible for a rectangle that is within the perimeter is 4 by 6 squares. So, the dimensions are 20xsqrt of 300//= //346.41. The area is also 20xsqrt of 300=346.41.//
 * B)What is the greatest area possible for a rectangle with this perimeter? What are the dimensions of this rectangle?**

C)What is the area of a rectangle with a side length of 12 meters? What is the area of the rectangle with a side length of 28 meters? //C)//A side length of 12 meters = 340m². A side length of 28 meters = 340m².

//D)Its the sqrt of 300x20 =////346.41//
 * D)What are the dimensions of the rectangle with an area of 300²m?**

//E)Its 40 because that is where it ends.//
 * E)****What is the fixed perimeter for the rectangles represented by the graph?**

__Problem 1.2 Follow-Up__

1) How do the shape and the special features you observed for the graph in Problem 1.2 appear in your table? //1)The rectangles that fit in the parabola are all on the table.//
 * Length of a side (m) || Area (m² ) ||
 * 0 || 0 ||
 * 1 || 11 ||
 * 2 || 20 ||
 * 3 || 27 ||
 * 4 || 32 ||
 * 5 || 35 ||
 * 6 || 36 ||
 * 7 || 35 ||
 * 8 || 32 ||
 * 9 || 27 ||
 * 10 || 20 ||
 * 11 || 11 ||

2)What is the fixed perimeter for the rectangles represented in the table? //2)24m² because 36m² is the highest area possible. So the side length must be 6m, so 6x4=24. So the fixed perimeter is 24m².//

3)What is the greatest area possible for a rectangle with this perimeter? //3)6x6.//

4)Approximate the dimensions of a rectangle with this fixed perimeter and an area of 16 square meters/ //4)The rectangle could be 4x4, 2x8, 1x16, 8x2 or 16x1.//