Name _______________________________________ Date __________________ Class __________________
Review for Mastery
Identifying Quadratic Functions
There are three steps to identify a quadratic function from a table
of ordered pairs.
Tell whether this function is quadratic. Explain.
x
 3  (5)   2
 1  (3)   2
1  (1)   2
312
y
5
191
3
59
1
1
1
11
3
95
Step 1: Check for a constant
change in x-values. Calculate
the second value minus the
first.
59  (191)   132
1  (59)   60
11  1  12
95  (11)  84
60  132  72
12 60  72
84  (12)  72
Step 3: Find the second
differences in y-values. If the
second differences are
constant, then the function is
quadratic.
Step 2: Find the first
differences in y-values.
If they are constant,
the function is linear.
This function is quadratic because the second differences are constant.
Tell whether each function is quadratic. Explain.
1.
x
y
 1  (4)  _____
4
43
16  43  _____
2  (1)  _____
1
16
7  16  _____
_____  _____  _____
2
7
_____  _____  _____
____________________
5
16
____________________
____________________
8
43
_____  _____  _____
____________________
____________________________________________________________________________________________
2.
3.
_____
_____
_____
_____
x
y
2
12
1
0
4
0
1
6
2
28
6
18
4
14
_____
2
10
0
6
2
2
_____
_____
y
_____
_____
_____
x
_____
____________________________________________
________________________________________
____________________________________________
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 1
Name _______________________________________ Date __________________ Class __________________
Review for Mastery
Identifying Quadratic Functions continued
To find the domain of a quadratic function, “flatten” the parabola toward the x-axis. To find the
range, “flatten” the parabola toward the y-axis. Then read the domain and range from the
inequality graphs.
Find the domain and range.
Flatten toward
the x-axis.
Flatten toward
the y-axis.
When the parabola is
flat, it looks like an
inequality graph with a
solid point at 3, and all
points above 3 are
shaded. So, the range
is “y  3.”
D: all real numbers
R: y  3
Imagine “flattening” each parabola to find the domain and range.
4.
5.
6.
D: _____________________
D: _________________
D: _________________
R: _____________________
R: _________________
R: _________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 1
Review for Mastery
1.3;
27
3; 9;
9; (27); 18
5; 2; 3;
16; 7; 9;
9  (9)  18
8  5  3; 43  16  27; 27  (9)  18
quadratic; the second difference are
constant.
2.1; 8
1; 4; 4
1; 6; 10
1; 22; 16
not quadratic the second differences are
not constant.
3.not quadratic it is linear.
4.all real numbers; y  0
5.all real numbers; y  2
6.all real numbers; y  15
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Algebra 1