Apollo 13 Quadratic Regression Project By Kanishka Sundar and Jimmy Christ Block 4

Given Chart Time(seconds) Distance from the moon(km) 1 425 2 356 3 293 236 8 68

Graph on calculator

Question 1:what does the data look like? Once we graphed the data we noticed that the line of the graph is descending.

Question 2: what does the x-axis represent(if you are sitting on the x-axis, where are you?) The x-axis represented the time(in seconds) If you are sitting on the x-axis you would be on the surface of the moon.

Question 3: Does it look like apollo 13 will hit the moon? It does indeed look like Apollo 13 will hit the moon!

Question 4: What is the value of a, B, and c? The value of a is 3 The value of b is -78 The value of c is 500 We did this on the calculator by finding the quadratic regression of best fit. Then calculated.

Question 5: How well does the graph fit the data points? It fits the data points perfectly.

Question 6: What is the minimum point of your quadratic function? First what we did is we took our a, b, and c values and made an equation. We plugged a, b, and c into the equation: ax^2+bx=c Then we took that equation and plugged it in to the quadratic formula 𝑥= −(−78)± (−78) 2 −4 3 (500) 2(3) From there we found our x-values :14.53,11.47. Then we added them and divided by 2. We plugged in what we got(13) and put it into the ax^2+bx=c equation and got -7 We found out that (13,-7) is our minimum point.

Question 7: Does your model tell you what happens to apollo 13 Question 7: Does your model tell you what happens to apollo 13?(crash, touches, or pulls away before?) We looked and found out that Apollo 13 crashes into the moon. If the x- axis is the moon, Apollo 13 goes to -7 past the x-axis. So that means Apollo 13 already hit the surface of the moon(x-axis) and crashed.

Question 8: where is the rocket at t=10 seconds? First we took 10 seconds and plugged it in as x in the ax^2+bx=c equation Then we got the answer 20 Then we put it in the proper unit. The answer is 20km

Question 9: what is the y-intercept? The y-intercept is the distance away from the moon

Question 10: At what time will Apollo 13 crash into the moon? We said 11.4 seconds. Because we figured out the 2 x-points and picked out the point that hit the moon first.

The end