Kinds of Parabola

Parabolas can be classified by 2 kinds of factors: 
1. By Concavity
2. By number of roots

1. By Concavity:
Concave up: a > 0
Concave down: a < 0

Concave Up: When a parabola opens upward and the constant a is greater than 0 then it is known as concave up. 

Concave Down: Similarly, when the constant a is lesser than 0 then it is known as concave down. 

This below image illustrates types of parabola by concavity:

Kinds of Parabola

2. By Number of Roots:
Other way of classifying parabola is by number of times the parabola intersects with the axis line.

2 roots: > 0
1 root: = 0 if the vertex touches the axis.
0 roots: < 0 if both x and y axis does not touch x or y axis. This could be found out with the help of the formula: b2-4ac.

This below image illustrates types of parabola by number of roots (intersecting with the axis):

Types of Parabola

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