AreaMy initial attempt was to create an x and y table so that I could find different points that I could plot on the graph in order to see if it was going to be a line or parabola. In order to create the x and y table, I first plugged in a number for x and solved the equation. Let's use 0 for an example. When you plug 0 into the equation, it looks like this, y = 16-0². 0 squared is still 0. 16 - 0= 16. So the X value is 0 and the Y value is 16. So I kept plugging in different numbers for x in order to get a y value. Now that I have the x and y values, I'm able to multiply them together to find the area of the rectangles inside the parabola.
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Largest AreaI knew that the biggest area of the rectangle was going to be between 2 & 3, so I tried numbers that were in-between those two numbers. I started off with 2.1 and worked my way up. As you can see on the left, the x value that got us the largest area was 2.3. In order to be more precise, I went to the nearest hundredth. So, I did the same process, I started off with 2.31 and worked my way up. After I found the largest area to the nearest hundredth, I stopped because my math teacher said that it was going to more time consuming and irrelevant if we go to the nearest thousandth. The value of x that got the largest area was 2.31.
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I knew that the largest perimeter was going to be in-between 0 and 1, so I used 0.5 to see where that got me and moved my way up, and down if needed. As you can see on the left, I listed out x values that were between 0-1, and I also wrote what the perimeter would be. Therefore, the value of x that got the largest perimeter was 0.5.
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