Question

Which function pass through the points (1, 4), (2, 9), and (3, 16)?

y = (x + 1)2
y = (x + 3)2
y = 7x - 5

Answer 1

`y= {(x+ 1)}^(2)`

Step-by-step explanation

The given points are:

(1, 4), (2, 9), and (3, 16)

It is obvious that the function is not linear because there is no constant difference among the y-values.

We can however manipulate the y-values to quickly identify the function.

`4 = {2}^(2) = {(1 + 1)}^(2)`

`9= {3}^(2) = {(2 + 1)}^(2)`

`16= {4}^(2) = {(3 + 1)}^(2)`

We can infer from the pattern that, the function is;

`y= {(x+ 1)}^(2)`