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course Mth 173
9/20 12:21 AM
The simulation athttp://phet.colorado.edu/sims/curve-fitting/curve-fitting_en.html
allows you to set points in the plane and fit linear, quadratic, cubic or quartic polynomials to those points.
To 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.
Linear - Straight line
Quadratic - Curve is closer to points
Cubic - curves are straight on points, different from the line, very curvy
Quartic - Same as cubic
Now repeat with five points (you can just add a point to the ones you already have). What happens?
Linear - Straight line
Quadratic - Curves toward line
Cubic - More curvy, curves through the line
Quartic - Curves are straight on points and very curvy through the line
Add another point and repeat. What happens?
Linear - Straight line
Quadratic - Starting curve is closer to line
Cubic - Ending curve is closer to line
Quartic - Almost straight line in the middle, curves downward on both ends.
Now put several points along an arc and see what happens.
With 14 points:
Linear - Straight line
Quadratic - Curve is close to line
Cubic - Curve is closer to line, curves toward and away from line in the middle while staying close.
Quartic - Almost straight line in the middle, curves downward on both ends.
Give your best responses, copy them into a Submit Work Form and submit.
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Good.
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