Quadratics
What are Parabolas?
Not all graphs can be straight lines and have a linear relation. Graphs which do not have a linear relation, may be curved. These curved lines are called parabolas.
To specify, unlike linear relations, which are modelled by the function y = mx + b, and form a straight line when graphed, non-linear relations form a curve when they are graphed.
The blue line in this graph is an example of a linear relation,
while the red curve is an example of a non-linear relation.
The curve that is formed by a non-linear relation in called a parabola.
Also, the most basic function of a parabola is y = x^2. This is also known as the parent function of parabolas, since it is the equation for the most basic parabola. All the other quadratic equations for a parabola are formed by adding different variations to this parent function. For instance, if 8 was added to the parent function, the new parabola will be translated 8 units up.
How to know if a relation is linear or not?
In order to know if a relationship is linear or quadratic, a table of values can be used. If the first differences in a table of values are constant (the same), it signifies that it is a linear relation and will form a straight line when graphed. On the other hand, when first differences are not constant, but the second differences are constant, it is a quadratic relationship. In cases when neither the first differences, nor the second differences are the same, the relationship is neither linear nor quadratic.
