Graphing quadratics with Transformations
Algebra III
Vertical Transformations f ( x)  x 2  k
f ( x)  x 2
Name:
g ( x)  x 2  1
h( x)  x 2  2
Complete the following table and graph all 3 functions on the same graph. Pay close attention to how
the output values change when a constant is added or subtracted from the parent function.
x
f ( x)  x 2
g ( x)  x 2  1
-2
-1
0
1
2
How does the k affect the output values on the table?
How does the k affect the graph of the function?
h( x)  x 2  2
Horizontal Transformations f ( x)   x  h 
2
g ( x)   x  1
f ( x)  x 2
h( x )   x  2 
2
2
Complete the following table and graph all 3 functions on the same graph. Pay close attention to how
the output values change when a constant is added or subtracted from the parent function.
x
f ( x)  x 2
g ( x)   x  1
-2
-1
0
1
2
How does the h affect the output values on the table?
How does the h affect the graph of the function?
2
h( x )   x  2 
2
Vertical Stretch/Shrink f ( x)  ax 2
g ( x)  2 x
f ( x)  x 2
h( x ) 
1 2
x
2
Complete the following table and graph all 3 functions on the same graph. Pay close attention to how
the output values change when a constant is added or subtracted from the parent function.
x
f ( x)  x 2
g ( x)  2 x
-2
-1
0
1
2
How does the a affect the output values on the table?
How does the a affect the graph of the function?
h( x ) 
1 2
x
2
Describe how each of the following functions compare to the parent function. Then graph each of the
quadratic functions. Plot at least 5 points.
1.
g ( x)  x 2  1
2.
Transformation:
3.
h( x )   x  2 
2
Transformation:
5.
f ( x) 
1 2
x
5
Transformation:
4. r ( x)   x  6 
2
Transformation:
6. f ( x)  ( x  2)2  3
Transformation:
6.
f ( x)  x 2  4
g ( x)   x  4   7
2
Transformation:
Transformation:
7. h( x)  ( x  1) 2  1
Transformation: