All parabolas are “U” shaped and
they will have a highest or lowest point that is called the vertex.
Parabolas may open up or down and may or may not have x-intercepts and
they will always have a single y-intercept.
Note as well that a parabola
that opens down will always open down and a parabola that opens up will always
open up. In other words a parabola will not all of a sudden turn around
and start opening up if it has already started opening down. Similarly,
if it has already started opening up it will not turn around and start opening
down all of a sudden.
The center line with each of
these parabolas is called the axis of symmetry. Every parabola has
an axis of symmetry and, as the graph shows, the graph to either side of the
axis of symmetry is a mirror image of the other side. This means that if
we know a point on one side of the parabola we will also know a point on the
other side based on the axis of symmetry.
Note that Vertex is at center of the
directix and latus rectum .
we can understand how to solve the parabola problem using some practice problems