Editing Parabola (section)

=== Parametric representation ===
An affine transformation of the Euclidean plane has the form <math>\vec x \to \vec f_0 + A \vec x</math>, where <math>A</math> is a regular matrix ([[determinant]] is not 0), and <math>\vec f_0</math> is an arbitrary vector. If <math>\vec f_1, \vec f_2</math> are the column vectors of the matrix <math>A</math>, the unit parabola <math>(t, t^2),\ t \in \R</math> is mapped onto the parabola
<math display="block">\vec x = \vec p(t) = \vec f_0 +\vec f_1 t +\vec f_2 t^2,</math>
where
* <math>\vec f_0</math> is a ''point'' of the parabola,
* <math>\vec f_1</math> is a ''tangent vector'' at point <math>\vec f_0</math>,
* <math>\vec f_2</math> is ''parallel to the axis'' of the parabola (axis of symmetry through the vertex).