Roller Coaster Project
To the teacher: This activity provides an opportunity for the students
to sketch a graph of a polynomial function with a multiplicity of roots.
They will identify where the graph is increasing and where it is decreasing
and write the general form of the polynomial in factored form.
Student Directions.
Sketch a roller coaster polynomial on a coordinate plane to include the
following characteristics:
1. Draw a roller coaster on a half sheet of poster board.
Be creative with your design. Be sure your graph is a function. The graph
may start above the ground and go below ground level (tunnels?). Use an
x-scale and a y-scale.
2. State the multiplicities of the roots: be sure to include at least
one double root and one triple root on the graph.
3. Color the path of the polynomial blue where it is increasing, red where
the graph is decreasing, and black where it is constant. Then state the
intervals for each.
4. State the intervals on the fromt of the poster where the function is
positive and where the function is negative.
5. Write the general form of the polynomial in factored form using k as
the scale factor. Find the value of k from the graph.
6. Give the sign of k and the degree of the polynomial.
Note to teacher:
A suggested grading scale:
10 pts. - neatness, attractiveness, creativity, follows directions
20 pts. - double roots and triple roots
20 pts. - colored sections of increasing, decreasing, and constant intervals
20 pts. - positive and negative intervals
20 pts. - factored form of the roller coaster
10 pts. - the value and sign of k, and the degree of the polynomial