Given the second difference, the table is quadratic.
What are linear and quadratic equations?
A linear function is a function that has a single variable raised to the power of 1. An example is x + 2. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. An example is 2x² + 10x + 25.
What are the first and second differences?
First differences:
21 - 11 = 10
35 - 21 = 14
53 - 35 = 18
75 - 53 = 22
Due to the fact that the first difference is not the same, the function is not a linear function.
Second difference:
14 - 10 = 4
18 - 14 = 4
22 - 18 = 4
Due to the fact that the second difference is fairly constant, the function is a quadratic function.
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