1.

Polynomials in real life  
2.

Linear polynomials  
3.

Quadratic polynomials  
4.

Intersections of lines and parabolas  
5.

Cubic polynomials  
6.

Polynomials of higher degree  
7.

Calculation of polynomials 
The program opens with examples of polynomial curves that appear in real life, including parabolic trajectories and the use of cubic splines in designing sailboats.
Polynomials are systematically classified by degree. Linear polynomials are discussed first; their graphs are straight lines of various slope.
Quadratic polynomials are discussed next. Their graphs are parabolas, the prototype being the graph of y = x^{2}. Animation shows how the Cartesian equation changes when the curve is translated vertically or horizontally or subjected to a vertical change of scale.
Cubic polynomials are treated next, with discussion of zeros, local maxima and minima, and points of inflection. There are three prototypes y = x^{3}, y = x^{3} + x, and y = x^{3}  x. All cubics can be obtained by horizontal or vertical translation or by horizontal or vertical change of scale, or by taking mirror images.
A similar discussion is given for quartics and higher degree polynomials, all of which have infinitely many prototypes.