Without seeing an image of the line or the parabola, you can tell whether or not the graph will show a linear or a quadratic.

In order to tell is by looking at the outputs.

When the outputs have values that create an arithmetic sequence, it is a linear relation.

y = 2x + 1

The x inputs are given and we can fill the equation and find the outputs

x = -3, y = -5

x = -2, y = -3

x = -1, y = -1

x = 0, y = 1

x = 1, y = 3

x = 2, y = 5

x = 3, y = 7

These outputs have a difference of +2. meaning it is an arithmetic sequences. This tells us it is a linear graph.

 

y = x²

The x inputs are given and we can fill the equation and find the outputs

x = -3, y = 9

x = -2, y = 4

x = -1, y = 1

x = 0, y = 0

x = 1, y = 1

x = 2, y = 4

x = 3, y = 9

The difference of these numbers are -5, -3, -1, +1, +3, +5

The difference of the difference is +2. When the second difference equals 2, it is a quadtratic.

 

This shows that every quadratic can identify as a quadratic if the difference of the difference is +2.