Type an equation for the following pattern

X: 1 | 2 | 3 | 4 | 5

Y: 1 | 4 | 9 | 16 | 25

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.