## Problem Statement

A rectangle has one corner on the graph of

**y=16-x^2**, another at the origin, a third on the positive y-axis, and the fourth on the positive x-axis. If the area of the rectangle is a function of x, what value of x yields the largest area for the rectangle?## Process

fig 1. fig 2.

Fig 1 is my first attempt of drawing the maximum rectangle based on the equation given to us y=16-x^2.

-from this attempt I knew I was dealing with a parabola, and the rectangle could only occupy one half of it on the first quadrant

-from this attempt I realized x would lie between 0-4 on the positive side.

Fig 2 shows the final and accurate diagram of the rectangle after solving for area perimeter.

-we created tables (fig . and . ), plugging in values to the x coordinates to find the highest values we could in area and perimeter (I show how I got the Area and Perimeter formula in fig 3 and 4).

Fig 1 is my first attempt of drawing the maximum rectangle based on the equation given to us y=16-x^2.

-from this attempt I knew I was dealing with a parabola, and the rectangle could only occupy one half of it on the first quadrant

-from this attempt I realized x would lie between 0-4 on the positive side.

Fig 2 shows the final and accurate diagram of the rectangle after solving for area perimeter.

-we created tables (fig . and . ), plugging in values to the x coordinates to find the highest values we could in area and perimeter (I show how I got the Area and Perimeter formula in fig 3 and 4).

Area To find the generalized function for maximum area, we took in account three things:
-x=base and y=height -the formula for area is A=(y)(x) -the given equation, y=16-x^2 Next, we plugged in the given equation into the formula for area and got AREA= 25-x^2After this we plugged in values for x, and got the highest value possible for perimeter. |
Perimeter To find the generalized function for maximum perimeter, we took in account three things:
-x=base and y=height -the formula for perimeter is P=2x+2y -the given equation, y=16-x^2 Next, we plugged in the given equation into the formula for perimeter and got PERIMETER= -2x^2+2x+50After this we plugged in values for x , and got the highest value possible for perimeter. |

## Solution

## Group test/ Individual test

Group test- my group and I prepared for this test by completing a practice problem the day before, similar to the one that would be on the test. We worked together and made sure to ask a lot of questions so we could thoroughly understand what was going on in each step and be prepared for the actual test.

On the actual test I think my group did a good job. I was constantly asking questions to make sure everyone was understanding. Although I felt some of us understood more than others I think we did a good job including everyone and making sure we all worked to get the best possible grade.

Overall, I had a positive experience with the group quiz.

Individual test- I worked through the individual test fast and with ease. The only part I choked up on was the honors portion, so I did my best and guessed.

On the actual test I think my group did a good job. I was constantly asking questions to make sure everyone was understanding. Although I felt some of us understood more than others I think we did a good job including everyone and making sure we all worked to get the best possible grade.

Overall, I had a positive experience with the group quiz.

Individual test- I worked through the individual test fast and with ease. The only part I choked up on was the honors portion, so I did my best and guessed.