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.


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!