Answer:
A (see attached)
Step-by-step explanation:
There are a couple of things you can look for to see if a table represents a quadratic function:
- do the values increase, then decrease, or vice versa
- do the differences have a constant difference.
Observation
In the first of the given tables, the f(x) values start out decreasing, and end up increasing. This is a good indication the table represents a quadratic function.
In the remaining tables, the f(x) values are always increasing.
- table 2: differences are always +2 (linear function)
- table 3: differences are always +4.5 (linear function)
- table 4: table values have a common ratio of 2 (exponential function)
Analysis
The f(x) values in table 1 have differences of ...
-3, -1, 1, 3
These values have differences of ...
2, 2, 2
The constant "second differences" mean that the function can be represented by a 2nd-degree polynomial, a quadratic. In fact, the equation for this table is ...
f(x) = x² +2
