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!