# Parabolas

## Common Parabola Features

There are two standard forms for the equation of a parabola, shown below.

Parabolas all share the following properties.

**One focus**and**one directrix****Eccentricity:***e*= 1This means that every point on the parabola is an equal distance from the focus and from the directrix.

**One vertex:**Located at the midpoint between the focus and the directrix**One axis of symmetry:**Passing through the vertex (and focus) and perpendicular to the directrix

We can divide parabolas into two types: those that **open up or down**, and those that **open left or right**.

The information we can find from the equation of each type of parabola is summarized in the table below.

## Graphs of Parabolas

### Parabolas Opening Up or Down

A parabola with an equation of this form **opens up or down**. Notice that *y *is written as a function of *x*.

Use the sliders below to change the values of *a*, *h*, and *k*, and see different parabolas that open up or down. The parabola is graphed along with its focus, directrix, and axis of symmetry.

### Parabolas Opening Right or Left

A parabola with an equation of this form opens right or left. Notice that *x** *is written as a function of *y*.

Use the sliders below to change the values of *a*, *h*, and *k*, and see different parabolas that open right or left. The parabola is graphed along with its focus, directrix, and axis of symmetry.