1. Core 2
Simple Transformations of Graphs
Translations
Translations
Draw a set of axes from −15 ≤ x ≤ 15 and −15 ≤ y ≤ 15 then
sketch the following quadratics
• y = (x + 1)(x + 3)
• y = (x + 3)(x + 5)
• y = (x + 10)(x + 8)
• y = (x − 5)(x − 7)
• y = x2 − 1
Write four more quadratics in the form y = (x + a)(x + b) that
have the same common property as the quadratics above.
H Mort 2012 1/7
2. Core 2
Simple Transformations of Graphs
Translations
Starting with the graph of y = f(x), then
0
• y = f(x) + b is a vertical translation
b
a
• y = f(x − a) is a horizontal translation
0
H Mort 2012 2/7
3. Core 2
Simple Transformations of Graphs
Translations
Starting with the graph of y = f(x), then
0
• y = f(x) + b is a vertical translation
b
a
• y = f(x − a) is a horizontal translation
0
Generally we write the two together
a
• y = f(x − a) + b is a translation by
b
This is the same format as the completed square form of a
quadratic, but it is true for all functions.
H Mort 2012 2/7
4. Core 2
Simple Transformations of Graphs
Translations
Exercise 5A, page 281
Questions: 1 to 3
H Mort 2012 3/7
5. Core 2
Simple Transformations of Graphs
Reflections
Reflections
Recall from GCSE that the graph of y = −x2 is the reflection of
the graph of y = x2 in the x-axis. In general;
• y = −f(x) is a reflection in the line y = 0 (the x-axis).
H Mort 2012 4/7
6. Core 2
Simple Transformations of Graphs
Reflections
Reflections
Recall from GCSE that the graph of y = −x2 is the reflection of
the graph of y = x2 in the x-axis. In general;
• y = −f(x) is a reflection in the line y = 0 (the x-axis).
Similarly,
• y = f(−x) is a reflection in the line x = 0 (the y-axis).
H Mort 2012 4/7
7. Core 2
Simple Transformations of Graphs
Reflections
Reflections
Recall from GCSE that the graph of y = −x2 is the reflection of
the graph of y = x2 in the x-axis. In general;
• y = −f(x) is a reflection in the line y = 0 (the x-axis).
Similarly,
• y = f(−x) is a reflection in the line x = 0 (the y-axis).
Example
Sketch the graphs of y = x3 + 2 and y = (−x)3 + 2.
H Mort 2012 4/7
8. Core 2
Simple Transformations of Graphs
One-way stretches
One-way Stretches
Example
y = x2 1 4 9 16
y = 10x2 10 40 90 160
Starting with y = f(x)
• y = df(x) is a stretch by a scale factor d in the y-direction
H Mort 2012 5/7
9. Core 2
Simple Transformations of Graphs
One-way stretches
One-way Stretches
Example
y = x2 1 4 9 16
y = 10x2 10 40 90 160
Starting with y = f(x)
• y = df(x) is a stretch by a scale factor d in the y-direction
1
• y = f(cx) is a stretch by a scale factor in the x-direction
c
x
• alternatively y = f is a stretch by a scale factor c in the
c
x-direction
H Mort 2012 5/7
