Exit Slip

The important concept of today's lesson was solving for the height of your can. Also putting the calculations from our can into a spreadsheet and labeling the columns. Another important concept was making a graph using our calculations from our can and labeling the graph as well.

The mathematical tool I used to today was a calculator. The calculator helped me calculate the height for all of the radiis. This mathematical tool made it easier for me because I just has to plug in my values into the calculator to get my answers and didnt have to use scrap paper.

Exit Slip 4/23/10

Today I helped some of my peers. I helped Ellen by explaining to her what was being asked of us. I also helped Sha'Eika find the Volume and Surface Area of her can.Today I was able to accomplish many things. I found all the measurements to my can by using a ruler. Also, I found the Surface Area and Volume of my can. The skills I learned today were how to find the height and diameter of a can or cylinder. I would use these skills when I want to build a cylinder model or in college when I have to do a project based on cylinders. For the moment I dont have any questions to ask because I understand everything that we are going to be doing for our PBAT.

Extra Credit.

The results from the two calculations are shown in Table 1. The first function is y1=4x^3+5 and the second function is y2=7x^3+100.

The first column contains some values for the independent variable x. The domain of these values: -25 to 25 were chosen randomly, first. I just wanted to make sure that when the graph is made the important parts would show. Some examples of the important parts are: the vertex, the roots, the local minimum, the local maximum, etc. The scale is set to 5.

These x-values were substituted into the function y1, and the results are displayed in the second column. Since y1 is a third degree polynomial or cubic function, the y-values first increase as the x-values increase from negative numbers to positive numbers. There is no vertex because this is a third degree polynomial. It is hard to tell the coordinates of the local minimum and maximum without a graph.

The y-values for y2=7x^3+100 are shown in the third column of Table 1. The y-values also increase as the x-values increase from negative to positive numbers.

Graphs Exit Slip

• The curvature of y2 compared to y1 is narrower, meanwhile y1 is wider. This is not a reflection on the x-axis. The reason why it is not a reflection is because the coeffiecients are different. The coefficient for y1 is 3 and the coefficient for y2 is -5.


• Compared to y1, y2's graph is shifted downward vertically, while y1 is shifted upward vertically. I see this in the graph by noting that the minimum point of y1 is (0,100) and the maximum point of y2 is (0,-100).
• There is no horizontal shift because the lines have the same pattern horizontally. Also the minimum and maximum line up at x=0.

Exit Slip

We can compare and contrast two functions in many ways, but I chose to compare and contrast my two functions by creating a graph. The two expressions I used were 2X^4 and -2X^4. Then I created a spreadsheet, which helped me a lot. In the spreadsheet one column was (X), the next one was Y1 and then Y2. The great thing about the spreadsheet was that when you went to a column all you had to do was drag the first number in the cell all the way down and the numbers were calculated for you. When that was done I had to graph my numbers, which was easy to do. After graphing the two functions I realzied that function y1 and y2 was a reflection of one another. Once the numbers were graphed I labeled my graph. I put the title, and labeled the x and y axis. I also had to change y1 and y2 to its functions. For example, for y1 I put 2*A2^4 and for y2 I put -2*A2^4. Once I plugged in those functions I then had to create a table on Google Docs. The table had the two functions, the highest , lowest, and constant term for each as well. For example, like for function y1 for the hghest term I put 2x^4 and then for y2 I put -2x^4. The next degree term and contant degree term was 0 for each functions.
In essence, by looking at my graph and table you can compare and contrast the two functions.

Exit Slip

1.One major thing i learned today was that i can create a graph on my Google spreadsheet. I think creating this Google spreadsheet makes it easier for me to do my graphs and plug in my functions.

2. I didn't have a major problem today. I understood everything i was doing and i found it to be very easy to create a Google spreadsheet.