Question

Write a function to represent the set of ordered pairs.

{(2, -2), (3, 8), (4, 22), (5, 40)}

Answer 1

y = 2x² - 10

Explanation:

We must find a pattern in the numbers. Set out the numbers in a table (Columns 1 and 2 in the table).

x y y/2 y/2 + 5

2 -2 -1 4

3 8 4 9

4 22 11 16

5 40 20 25

It looks like all y-values are multiples of 2.

Let's divide them by 2 (Column 3).

The numbers don't increase evenly. We may have a quadratic function.

If we add 5 to each quotient, we get a set of values equal to x² (Column 4).

y/2 + 5 = x²

y + 10 = 2x²

y = 2x² - 10

The function is y = 2x² - 10.