structural:reformatting, information:classification
As a graph of a function

The previous section shows that any parabola with the origin as vertex and the y axis as axis of symmetry can be considered as the graph of a function

For a > 0 {\displaystyle a>0} the parabolas are opening to the top, and for a < 0 {\displaystyle a<0} are opening to the bottom (see picture). From the section above one obtains:

For a = 1 {\displaystyle a=1} the parabola is the unit parabola with equation y = x 2 {\displaystyle y=x^{2}}.Its focus is (0, 1 4) {\displaystyle \left(0,{\tfrac {1}{4}}\right)}, the semi-latus rectum p = 1 2 {\displaystyle p={\tfrac {1}{2}}}, and the directrix has the equation y = − 1 4 {\displaystyle y=-{\tfrac {1}{4}}}.

The general function of degree 2 is

Completing the square yields

which is the equation of a parabola with