# exploring transformations of parent functions

```MCR3U1
U2L6
EXPLORING TRANSFORMATIONS
(of the Parent Functions)
PART A ~ REVIEW OF TRANSFORMATIONS (QUADRATIC FUNCTIONS)
Sketch the graph of y = x2:
y
ordinate differences:
the differences in the
y-coordinates
V(0,0)
OD: 1, 3, 5, …
x
The graph of y = x2 can be transformed as follows:
𝑓 (𝑥 ) = 𝑎(𝑥 − 𝑑)2 + 𝑐
 vertical stretch
(|a| &gt; 1)
 vertical compression
(0 &lt; |a| &lt; 1)
 reflection (x-axis)
(a &lt; 0)
Example 
 horizontal translation
(+) move left
(–) move right
 vertical translation
(+) move up
(–) move down
vertex: (d,c) axis of symmetry: x = d
max (a &lt; 0) or min (a &gt; 0) value: y = c
Describe the transformations that have occurred to 𝑓(𝑥) = 𝑥 2 to obtain
the function 𝑓(𝑥) = −3(𝑥 − 2)2 + 5.
MCR3U1
U2L6
Example 
Sketch each of the following functions:
a) 𝑓(𝑥) = 2(𝑥 − 3)2 − 5
vertex:
____________________
axis of symmetry:
____________________
direction
of opening:
____________________
max/min value:
____________________
range:
____________________
y
x
y
1
b) 𝑓(𝑥) = − (𝑥 + 1)2 + 3
2
vertex:
____________________
axis of symmetry:
____________________
direction
of opening:
____________________
max/min value:
____________________
range:
____________________
Example 
a)




xx
Write an equation for each of the following quadratic functions:
HT left 6 units
VT up 2 units
VC by a factor of &frac12;
reflected in the x–axis
b)
HOMEWORK: Sketch a graph of each of the following quadratic functions:
a) 𝑓(𝑥) = (𝑥 − 4)2
1
d) 𝑓(𝑥) = 𝑥 2 + 2
2
b) 𝑓(𝑥) = (𝑥 + 3)2 − 4
e) 𝑓(𝑥) = −3(𝑥 − 2)2
c) 𝑓(𝑥) = 2(𝑥 − 3)2 + 1
f) 𝑓(𝑥) = −(𝑥 + 1)2 − 2
MCR3U1
U2L6
PART B ~ REVIEW OF THE FIVE PARENT FUNCTIONS
LINEAR FUNCTION
𝑓(𝑥) = 𝑥


y
𝑓(𝑥) = 𝑥 2
y
x
RECIPROCAL FUNCTION
1
𝑓(𝑥) =

y

𝑥
ABSOLUTE VALUE FUNCTION
𝑓(𝑥) = | 𝑥 |
y
x
SQUARE ROOT FUNCTION
𝑓(𝑥) = √𝑥

x
y
x
x
```