help me pleaseee

Question

The table below shows a relationship between values of x and y. Write an equation that describes the relationship for the values in the table.

Answer 1

The numbers in the y row seem to increase a lot faster than the ones in the x row. And they seem to increase about as fast as the square. But squaring x doesn't seem to grow quite fast enough to get y (2 squared is 4 instead of 6, 3 squared is 9 instead of 16, etc.). What works for the start of this sequence is to take twice the square of x, and subtract 2. So:

y = 2 x² - 2

We'll have to assume this relationship also works for further numbers in the sequence, based on this start.