  Planar quadratic differential systems occur in many areas of applied
mathematics. Although more than one thousand papers have been written on these
systems, a complete understanding of this family is still missing. Classical
problems, and in particular, Hilbert's 16th problem, are still open for this
family. In this article we make a global study of the family QTN of all real
quadratic polynomial differential systems which have a semi-elemental triple
node (triple node with exactly one zero eigenvalue). This family modulo the
action of the affine group and time homotheties is three-dimensional and we
give its bifurcation diagram with respect to a normal form, in the
three-dimensional real space of the parameters of this form. This bifurcation
diagram yields 28 phase portraits for systems in QTN counting phase portraits
with and without limit cycles. Algebraic invariants are used to construct the
bifurcation set. The phase portraits are represented on the Poincar\'e disk.
The bifurcation set is not only algebraic due to the presence of a surface
found numerically. All points in this surface correspond to connections of
separatrices.
