1. Math Project 2 By: Holden Greene and Joseph Young

2. Part 1 We plugged the numbers from the table into the formula that was given. h=at^2+bt+c 1) 23645=4a+2b+c 2) 32015=400a+20b+c 3) 33715=1600a+40b+c We plugged the numbers from the table into the formula that was given. h=at^2+bt+c 1) 23645=4a+2b+c 2) 32015=400a+20b+c 3) 33715=1600a+40b+c

3. Part 2 First we subtracted problem 1 from problem 2. Using Elimination to get the answer. 32015=400a+20b+c - 23645=-4a-2b-c ---------------------------- 8370=396a-18b This answer becomes #4. First we subtracted problem 1 from problem 2. Using Elimination to get the answer. 32015=400a+20b+c - 23645=-4a-2b-c ---------------------------- 8370=396a-18b This answer becomes #4.

4. Part 2 Continued We then subtracted problem 2 from 3 and used elimination to solve it again. 33715=1600a+40b+c -32015=-400a-20b-c --------------------------- 1700=1200a+20b This answer becomes problem 5. We then subtracted problem 2 from 3 and used elimination to solve it again. 33715=1600a+40b+c -32015=-400a-20b-c --------------------------- 1700=1200a+20b This answer becomes problem 5.

5. Part 2 Continued We then used elimination with problems 4 and 5. We multiplied 4 by 10 and 5 by -9 in order to eliminate. 8370=396a+18b (10)= 83700=3960a+180b 1700=1200a+20b (-9)= -15300=-10800a-180b ----------------------------------------------------------- 68400=-6840a then divide by -6840 which gives you an answer of -10=a We then used elimination with problems 4 and 5. We multiplied 4 by 10 and 5 by -9 in order to eliminate. 8370=396a+18b (10)= 83700=3960a+180b 1700=1200a+20b (-9)= -15300=-10800a-180b ----------------------------------------------------------- 68400=-6840a then divide by -6840 which gives you an answer of -10=a

6. Part 2 Continued We then plugged the A(-10) that we got from our earlier solution into problem 5. 1700=1200(-10)+20b 1700=-12000+20b 13700=20b _____________________ The answer that we got was 685=b. We then plugged the A(-10) that we got from our earlier solution into problem 5. 1700=1200(-10)+20b 1700=-12000+20b 13700=20b _____________________ The answer that we got was 685=b.

7. Part 2 Continued We then plugged our answers for A(-10) and B(685) into our first problem to find C. 23645=4(-10)+2(685)+C 23645=-40+1370+C 23645+40-1370=C _____________________ The answer that we got was C=22315. We then plugged our answers for A(-10) and B(685) into our first problem to find C. 23645=4(-10)+2(685)+C 23645=-40+1370+C 23645+40-1370=C _____________________ The answer that we got was C=22315.

8. Part 2 Summary In summation of our work the answers that we got were: A=-10 B=685 C=22315 In summation of our work the answers that we got were: A=-10 B=685 C=22315

9. Part 3 We then plugged our numbers into our equation h=at^2+bt+c. This gave us h=-10t^2+685t+22315 We then plugged our numbers into our equation h=at^2+bt+c. This gave us h=-10t^2+685t+22315

10. Part 4 We found the maximum value of the quadratic function by solving for Y from our equation in Part 3. We are then able to come up with our maximum

11. The Solving of Part 4 y=-10t^2+685t+22315 y=-10(t^2-68.5t+1173.0625)+22315+- 10(1173.0625) 22315+11730.625 y=-10(t-34.25)^2 y=-10(t-34.25)^2+34045.625 This gives us our graph and the parabola that we will be using for our answer. A=-10 X=T H=- 34.25 K=34045.625 y=-10t^2+685t+22315 y=-10(t^2-68.5t+1173.0625)+22315+- 10(1173.0625) 22315+11730.625 y=-10(t-34.25)^2 y=-10(t-34.25)^2+34045.625 This gives us our graph and the parabola that we will be using for our answer. A=-10 X=T H=- 34.25 K=34045.625

12. Part 5, The Graph We used this equation to get our graph y=-10(t- 34.25)^2+34045.625. Maximum= 34045.625 Vertex=(34.25, 34045.625) Axis X= 34.25 We used this equation to get our graph y=-10(t- 34.25)^2+34045.625. Maximum= 34045.625 Vertex=(34.25, 34045.625) Axis X= 34.25

13. Part Five, The Graph Continued

14. Part 6 Yes it changed our minds completely about the purpose of math and the way that it can be used in real world situations. It really enlightened our thinking towards the real world examples that math participates in and give credence towards math and the purpose that it serves in the world outside of the boundaries of our educational facilities. Math is an ever important factor in life more so probably then English or a history or social studies class of some sort. This is due to the ever present factor of math in our life while rarely must we remember history or the role that it plays in our world. And english is obviously a very unneeded skill that will serve no purpose later in life, because very rarely do we use english in our lives. That is why math is very important to us and is how this project has revealed to us the importance of math in the real world. We use math alot more then any other subject.