Apollo 13 Quadratic Regression Project By Kristin Rice

Apollo 13: Quadratic Regression Project By Kristin Rice, Taylor Fischer, and Morgan Fischer

Scenario During the Apollo 13 mission the moon, the oxygen tanks exploded. The team was given two options to abort the mission. Option 1 was that they would turn on the “retro rockets” and head directly back to earth. Option 2 used the gravitational pull of the moon to slingshot the astronauts back home. For their mission the team used Option 2 and they were successful. If the astronauts used Option 1 would they have been successful?

What does the x-axis represent? Time Does it look like the Apollo 13 will hit the moon? Yes

What are the values of the variables in the Quadratic Equation? A= 3 B= -78 C= 500 The Quadratic Equation: 3 x²-78 x+500

How well does the graph fit the data points? Almost perfectly, all of the points are on the graph except one which is slightly to the left of the line.

What is the minimum point of your Quadratic Function? -7 -b/2 a 78/2(3) = 78/6 = 13 3(13)²-78(13)+500 = -7 x= -7

Does your model tell you that Apollo 13 crashed into the surface of the moon, just touches the surface, or pulls away before reaching It crashed because the y value, which is the distance from the moon, is negative. surface? Approximately where is the rocket at t=10 seconds, according to the 20 kilometers from the moon model?

What is the y-intercept? What does this point represent in terms of this The y-intercept is the distance in kilometers from the moon. situation? At what time will the Apollo 13 crash into the moon? _____ 11. 47 seconds X= 78+9. 17 / 6 X= 78+ √ 78 -4(3)(500) / 2(3) ____ X= 78+ √ 6084 -6000 / 6 __ X= 78+ √ 84 / 6 X=14. 53 X= 78 -9. 17 / 6 X= 11. 47

Conclusion The astronauts cannot use Option 1, because they will crash into the moon if that option is used.