Additional 2D Constructions

Comprehension Questions

Math 250 - Math with Mathematica
Christopher Hanusa

9-1. Draw the curve y=(x^3)+2(x^2)+x+1 and place a point on it.

Important reminder: When you need to combine multiple Graphics objects, use the Show command.

9-2. Use a BSplineCurve command to make a circle-like curve.

9-3. Create a two-dimensional region that has the curve from Question 9-2 as its boundary.

9-4.  Plot the two curves y=(Sqrt[x]) and y=(x^2) for x between 0 and 1 on the same set of axes.

9-5.  Use RegionPlot to draw the region that is between the two curves from Question 9-4.

Challenge Questions

9-X1.  Use a parametric curve to recreate the polar plot of r=cos(3θ):

Hint:

Recall that to convert from polar coordinates to cartesian coordinates you can use x=r cos(θ) and y=r sin(θ).

9-X2.  Create a curve that looks like rabbit ears, perhaps something like this:

9-X3.  Create the following picture: