 An
algebraic operation which alters the
shape, position and/or size of a shape or
function.
 There
are SIX types of transformations which
we will study in Math 12 and Pre-Calculus 12.






Reflection in X
Vertical Stretch
Vertical Translation
Reflection in Y
Horizontal Stretch
Horizontal Translation
 Reflection



Rx
A transformation which reflects a coordinate,
shape or function across the X-axis.
(x,y)->(x,-y)


in X:
The value of the x-coordinate remains constant while
the y-coordinate becomes it’s opposite.
E.g. (2,1) when reflected across the x-axis
becomes (2,-1)
 Reflection



Ry
A transformation which reflects a coordinate,
shape or function across the Y-axis
(x,y)->(-x,y)


in the Y-axis
The value of the y-coordinate remains constant while
the value of the x-coordinate becomes its opposite.
E.g. (2,1) when reflected across the y-axis
becomes (-2,1)

Vertical Stretch
VS
 A transformation which may compress or expand a
shape or function in the vertical direction.


Horizontal Stretch
HS
 A transformation which may compress or expand a
shape or function in the horizontal direction.

Stretches are multiplied
 Vertical



Translation:
VT
A transformation which shifts a shape or function
vertically
Does NOT alter the shape of the figure or
function.
 Horizontal



Translation:
HT
A transformation which shifts a shape or function
horizontally
Does NOT alter the shape of a figure or function
Translations are added
1
2
 ( y  k )  ( x  h)
a

 the reflection in the X-axis, Rx
a
– the vertical stretch, VS
 k – the vertical translation, VT
 h – the horizontal translation, HT
 This the rearrangement of quadratics’
2
general form: y  ax  bx  c
 The
vertex is the maximum or minimum
coordinate of a quadratic function.
 The vertex can be found from the
transformational form of a quadratic.


(HT,VT)
(h,k)
1
 ( y  k )  ( x  h) 2
a
 The
vertex can also be found using the
formula: x   b
2a
y 3 x
2
y  2  ( x  5)
2
1
2
 ( y  2)  ( x  1)
5
( y  2)  ( x  3)
2
1
2
 ( y  5)  ( x  3)
3
 4( y  1)  ( x  6)
2