# How to analyze an equation of a parabola?

To analyze an equation of a parabola their special characteristics that can be looked at to determine what type of parabola it is.

Example:

Let's get this equation to something that's understandable by understanding what type of parabola it is, recall our cheet sheet helps with this.

Let `4a = 8`

divide by `4`

then `a = 2`

Since nothing is being added to the constant `8x`

then the vertex is located at `(0,0)`

. The focus is located at `(a,0)`

which is `(2,0)`

. The directrix is located at `x = -2`

.

Now the last part remaining is to solve for two points on the graph, let's use the focus value of `a`

to determine those points.

Now the values for graph are.

Points: `(2,-4)`

`(2,+4)`

Vertex: `(0,0)`

Focus: `(2,0)`

Directrix: `(-2,0)`

Now the easy part is to graph it!