Math 1330 – Section 8.1
Parabolas
Next, we’ll look at parabolas. We previously studied parabolas as the graphs of quadratic
functions. Now we will look at them as conic sections. There are a few differences. For
example, when we studied quadratic functions, we saw that the graphs of the functions
could open up or down. As we look at conic sections, we’ll see that the graphs of these
second degree equations can also open left or right. So, not every parabola we’ll look at
in this section will be a function.
We already know that the graph of a quadratic function
f x
ax bx
c( ) = + +
2
is a
parabola. But there is more to be learned about parabolas.
Definition: A parabola is the set of all points equally distant from a fixed line and a
fixed point not on the line. The fixed line is called the directrix. The fixed point is called
the focus.
The axis, or axis of symmetry, runs through the focus and is perpendicular to the directrix.
The vertex is the point halfway between the focus and the directrix.
We won’t be working with slanted parabolas, just with “horizontal” and “vertical”
parabolas.
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