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LESSON
9-1
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.
 3  (5)   2
 1  (3)   2
1  (1)   2
312
x
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
60  132  72
1  (59)   60
12 60  72
11  1  12
84  (12)  72
95  (11)  84
Step 2: Find the first
differences in
y-values. If they are
constant, the function
is linear.
Step 3: Find the second
differences in y-values.
If the second differences are
constant, then the function is
quadratic.
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
_____
1
6
2
28
4
0
_____
_____
_____
x
y
6
18
_____
4
14
_____
2
10
0
6
2
2
_____
_____
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A21
Holt McDougal Algebra 1
LESSON
9-1
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.
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.”
Flatten toward
the y-axis.
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.
A21
Holt McDougal Algebra 1