Families of lines and parabolas
Slide the parameter of a family, find the carrier graph of the vertices and solve the tangent problem with the discriminant.
- France: grade 10
- Germany: grade 9
- Syria: grade 10
- Palestine: grade 9
- Ukraine: grade 8
Guide
A Schar (family) is a set of graphs that differ in a parameter: the Parallelenschar y = 2x + t has the same m and any t; the Parabelschar y = x² + p x + 1 has a vertex that moves with p.
The vertices of a Parabelschar lie on a Trägergraph. You find it by the Parameterverfahren: write x_S and y_S with the parameter, solve x_S for the parameter and put it into y_S.
This studio belongs to the Realschule syllabus. The discriminant D = b² – 4ac decides the number of common points of a line and a parabola.