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course Mth 173
10/12 8
PHET SIMULATIONTo set a point you grab one from the little basket near the top right of the graph area.
Set four points more or less along a straight line, but don't make the pattern too straight. Fit a linear, then a quadratic, then a cubic, then a quartic polynomial to the data. Pay attention to whether the curve gets closer to the line, on the average, at each step. Report what you see.
When fitting a straight line to my chosen 4 points, the accuracy is around 10. When using a quadratic function the accuracy increases slightly to 11. When using a cubic function the accuracy goes to 100, because all 4 points are on the line. When using a quartic function, I get similar results to the cubic. The 5 variables of the quartic is not necessary to represent the 4 original points, so the last term is 0.
Now repeat with five points (you can just add a point to the ones you already have). What happens?
When fitting a straight line to my chosen 5 points, the accuracy is around 7. When using a quadratic function, the accuracy increases to 9. When using a cubic function the accuracy increases to 15. When using a quartic function the accuracy is 100 because all points are on the line.
Add another point and repeat. What happens?
When fitting a straight line to my chosen 6 points, the accuracy is around 9. When using a quadratic function, the accuracy increases to 15. When using a cubic function the accuracy drops to 5 . When using a quartic function the accuracy increases to 9.
Now put several points along an arc and see what happens.
When fitting a straight line to my chosen 3 points, the accuracy is around 30. When fitting a quadratic, cubic, and quartic to my 3 points, the accuracy is 100.
Give your best responses, copy them into a Submit Work Form and submit.
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Good.
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critiqued_student work modified 141012__________
critiqued_student work modified 141012__________
critiqued_student work modified 141012__________