Identifying a possible non-linear rule for a given table of values

Further examples of identifying a non-linear rule for a given table of values

Question 2

x	0	1	2	3
y	−3	−7	−19	−39

Which equation possibly describes the relationship between x and y ?

y = −4x − 3

y = 4x² − 3

y = −4x² − 3

y = 4x − 3

 

Solution

First step

As x increases by 1, y does not decrease by the same amount each time. Hence the rule is not linear and we can eliminate y = −4x − 3 and y = 4x − 3 as possibilities.

y decreases by 4, then 12 and then 20.

Second step

All of the remaining rules are of the form y = ax² + b. That leaves us with y = −4x² − 3 and y = 4x² − 3. These both have an x² term and so are quadratic equations.

Third step

When x = 0, y = − 3. The constant term is − 3.

y = ax² − 3

When x = 1,

−7 = a − 3

a = −4

The answer is y = −4x² − 3.

Detailed description of video

Alternative solution: by substitution

Further example, Q3