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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:
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):
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