Linear/quadratic/exponential Tables Worksheet With Answer Key

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LINEAR/QUADRATIC/EXPONENTIAL TABLES
HOW TO RECOGNIZE THE TYPE OF GRAPH FROM A TABLE
To recognize if a function is linear, quadratic (a parabola), or exponential without an
equation or graph, look at the differences of the y-values between successive integral
x-values. If the difference is constant, the graph is linear. If the difference is not
constant but the second set of differences are constant, the graph is quadratic. If the
differences follow a pattern similar to the y-values, the graph is exponential. See the
examples below for clarity.
Examples
Based on each table, identify the shape of the graph.
Example 1
!
!
!
x
2
1
0
1
2
3
3
!
!
!
!
1
7
5
3
1
3
5
y
2
2
2
2
2
2
The difference in y-values is always two, a constant.
The graph is linear and is verified at right.
Example 2
!
!
!
x
2
1
0
1
2
3
3
9
4
1
0
1
4
9
y
!
!
!
5
3
1
3
5
1
2
2
2
2
2
The first difference in y-values is not constant but the
second difference is. The graph is quadratic and is verified at right.
Example 3
!
!
!
x
2
1
3
0
1
2
3
1
1
1
1
2
4
8
y
8
4
2
1
1
1
1
2
4
8
4
2
The difference in y-values follows a pattern similar to
the y-values. The graph is exponential and is verified at right. (In this case, the
difference pattern was exactly the same as the y-values. This is not always necessary.)

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