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
0
