Question

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

Answer 1

ANSWER

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

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;

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