Quadratics
A quadratic relationship is shown when the outcome of the expression makes a parabola. The picture below shows a Parabola.
A quadratic relation can be written in many ways. But there are three ways you should learn first. The first way is Vertex Form, the second way is Factored Form and the third way is standard form.
Vertex Form is written like this: y= a(x-h)^2 + K
Factored form is written like this: y= a(x-r)(x-s)
Standard Form is written like this: y =ax^2 + bx + c
You can tell if it is a quadratic relation or not by finding out the first and second differences. If all the first differences are the same then it is linear relation. If the first differences aren't the same, you should look at the second differences, if they are the same it will be a quadratic relation. If it doesn't have the same first or second differences then it is neither.
Here is an example:
In the first image the first differences are the same, therefore making it a linear relation.
Vertex Form is written like this: y= a(x-h)^2 + K
Factored form is written like this: y= a(x-r)(x-s)
Standard Form is written like this: y =ax^2 + bx + c
You can tell if it is a quadratic relation or not by finding out the first and second differences. If all the first differences are the same then it is linear relation. If the first differences aren't the same, you should look at the second differences, if they are the same it will be a quadratic relation. If it doesn't have the same first or second differences then it is neither.
Here is an example:
In the first image the first differences are the same, therefore making it a linear relation.
This second picture is an example of all the second differences being the same, therefore making a quadratic relation.