Answer: y = x²
Explanation:
x | y
1 | 1
2 | 4
3 | 9
4 | 16
5 | 25
The x-coordinates increase by 1 unit. Now, look at the intervals of the y-coordinates:
1 to 4 = 3
4 to 9 = 5
9 to 16 = 7
16 to 25 = 9
Their intervals are not equal so it is not a linear equation (y = x). So, go one more generation and compare the intervals above:
3 to 5 = 2
5 to 7 = 2
7 to 9 = 2
Their intervals are equal so it is a quadratic equation (y = x²).
Note: First generation is a linear equation.
Second generation is a quadratic equation.
