PHet 2

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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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