Problem Statement
A rectangle has one corner on the graph of y=16-x^2, another at the origin, 1/3 on the positive x-axis, and the fourth on the positive y-axis. If the area of the rectangle has a function of x, what value of x yields the largest area for the rectangle?
Process
Understanding the Maximum Rectangle Problem...
My group and I read the problem and knew that this rectangle will be located in the first quadrant in the graph by asking a question. Without really thinking, we thought the rectangle will look like Figure 1, a rectangle touching the y and x axis.
We looked at the problem twice and we knew something was wrong...This problem will have a parabola, inside that parabola will be the maximum rectangle we've been looking for. One of my partners used the resource, Desmos, to locate the parabola. (Figure 2) |
Solving the Problem...
I knew that on a T table we could only plug in the numbers 1-4 for x. The maximum rectangle will be located in the parabola and the parabola intercepts (4,0) in the x-axis.
Our formulas for calculating the area... The formula A=LxW represents the calculations of area in a rectangle/square. 16-x^2= the width to figure out the area of our rectangle. x was our length of the rectangle x(16-x^2) was our area formula (Figure 3) I listed all the possible outcomes for x, 2 and 3 gave me the highest area so far. We knew that our highest area will be a decimal between 2 and 3. (Figure 4) 2.3 was our highest point. We plugged it in... 2.3(16-2.3^2)=24.633 24.633 is the highest area. (2.3 for x, 10.71 for y) |
How about the Maximum Perimeter?
Group Test & Individual Quiz
At first, our group didn't seem to work together at the same pace. As a person, I was okay with it because those who can exceed shouldn't be held back. Although, my only concern was the group test. Working together to help each other grow was the purpose. Not to leave one another behind. In order to prepare, we did a practice test with each other. It didn't go as well as we expected.
Although, in the group quiz everyone seemed to take it seriously. My group members waited for one another and asked if everyone understood. It was a positive learning experience and I was surprised yet proud of everyone around me. I personally was confused at times but I wasn't afraid to ask questions. Politely and as simple my group members can explain, they helped me understand the problem before us.
I felt that I understood the problem but I couldn't explain it to another. In the group quiz we didn't solve for the perimeter. Overall, I had an average experience but I enjoyed watching and hearing other peoples thinking.
Reflection
What pushed my thinking was my classmates. They helped me out when I needed it. I learned how to be a better group member and motivate those around me. If I had to grade myself, I would give myself a B+ because I tried my best, but didn't achieve full acuracy.
Although, in the group quiz everyone seemed to take it seriously. My group members waited for one another and asked if everyone understood. It was a positive learning experience and I was surprised yet proud of everyone around me. I personally was confused at times but I wasn't afraid to ask questions. Politely and as simple my group members can explain, they helped me understand the problem before us.
I felt that I understood the problem but I couldn't explain it to another. In the group quiz we didn't solve for the perimeter. Overall, I had an average experience but I enjoyed watching and hearing other peoples thinking.
Reflection
What pushed my thinking was my classmates. They helped me out when I needed it. I learned how to be a better group member and motivate those around me. If I had to grade myself, I would give myself a B+ because I tried my best, but didn't achieve full acuracy.