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

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

3. Graph on calculator

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

5. 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.

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

7. 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.

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

9. 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, 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.

10. 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.

11. 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

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

13. 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.

14. The end