Quadratic Function Transformations
Quadratic Function Transformations
Quadratic Function Transformation Exercise
The quadratic function is y = x2 , denoted by function g.
The transformed basic function is y = a(bx - h)2 +k
Note: The 'slider' feature on the x-y coordinate plane can be used to change the a, b, h, and k values
for the following exercises. To do so, place the cursor and hold it on the dot of the slider and
slide it to the desired m and b values.
To move the slider to a different location on the x-y plane, place the cursor and hold it on the line
of the slider and move it to the desired location.
Note: You can zoom in or out with the mouse.
Exercise 1
Perform the following quadratic function transformation:
Vertical shift of 3 units up.
The new function is y=x2 +3 , denoted by function f.
Set a=1. Set b=1.
Set h=0 since there is no horizontal shift
Set k=3 which represents the vertical shift of 3 units up.
Observe the transformation of the quadratic function.
Exercise 2
Perform the following quadratic function transformation:
Vertical shift of 3 units down.
The new function is y=x2 - 3 , denoted by function f.
Set a=1. Set b=1.
Set h=0 since there is no horizontal shift
Set k= - 3 which represents the vertical shift of 3 units down.
Observe the transformation of the quadratic function.
Exercise 3
Perform the following quadratic function transformation:
Horizontal shift of 3 units to the right.
The new function is y=(x-3)2 , denoted by function f.
Set a=1. Set b=1.
Set h=3 which represents the horizontal shift of 3 units to the right.
Set k=0 since there is not vertical shift.
Observe the transformation of the quadratic function.
Exercise 4
Perform the following quadratic function transformation:
Horizontal shift of 3 units to the left.
The new function is y=(x+3)2 , denoted by function f.
Set a=1. Set b=1.
Set h=- 3 which represents the horizontal shift of 3 units to the left.
Set k=0 since there is not vertical shift.
Observe the transformation of the quadratic function.
Exercise 5
Perform the following quadratic function transformation:
Vertical shift of 3 units up plus a horizontal shift of 3 units to the right.
New function: y = (x-3)2 +3 , denoted by function f.
Set a=1. Set b=1.
Set h=3 which represents the horizontal shift of 3 units to the right.
Set k=3 which represents the vertical shift of 3 units up.
Observe the transformation of the quadratic function.
Exercise 6
Perform the following quadratic function transformation:
Vertical shift of 3 units down plus a horizontal shift of 3 units to the left.
New function: y = (x+3)2 - 3 , denoted by function f.
Set a=1. Set b=1.
Set h=- 3 which represents the horizontal shift of 3 units to the left.
Set k=- 3 which represents the vertical shift of 3 units down.
Observe the transformation of the quadratic function.
Exercise 7
Perform the following quadratic function transformation:
Vertical shift of 3 units down plus a horizontal shift of 3 units to the right.
New function: y = (x - 3)2 - 3 , denoted by function f.
Set a=1. Set b=1.
Set h= 3 which represents the horizontal shift of 3 units to the right.
Set k=- 3 which represents the vertical shift of 3 units down.
Observe the transformation of the quadratic function.
Exercise 8
Perform the following quadratic function transformation:
Vertical shift of 3 units up plus a horizontal shift of 3 units to the left.
New function: y = (x + 3)2 + 3 , denoted by function f.
Set a=1. Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the quadratic function.
Exercise 9
Perform the following quadratic function transformation:
Vertical stretch by a factor of 3.
New function: y = 3 x2 , denoted by function f.
Set a=3. Set b=1.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the quadratic function.
Exercise 10
Perform the following quadratic function transformation:
Vertical shrink by a factor of 1/3.
New function: y = 1/3 x2 , denoted by function f.
Set a=1/3. Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the quadratic function.
Exercise 11
Perform the following quadratic function transformation:
Vertical shift of 3 units up, horizontal shift of 3 units to the left
and a vertical stretch by a factor of 2 .
New function: y = 2(x + 3)2 + 3 , denoted by function f.
Set a=2. Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the quadratic function.
Exercise 12
Perform the following quadratic function transformation:
Vertical shift of 3 units up, horizontal shift of 3 units to the left,
a vertical shrink by a factor of 1/2 .
New function: y = 1/2(x + 3)2 + 3 , denoted by function f.
Set a=2. Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the quadratic function.
Exercise 13
Perform the following quadratic function transformation:
Horizontal stretch by a factor of 1/3.
New function: y = (1/3x)2 , denoted by function f.
Set a =1. Set b=1/3.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the quadratic function.
Exercise 14
Perform the following quadratic function transformation:
Horizontal shrink by a factor of 3.
New function: y = (3x)2 , denoted by function f.
Set a =1. Set b = 3.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the quadratic function.
Exercise 15
Perform the following quadratic function transformation:
Reflection over the x-axis.
New function: y = - x2 , denoted by function f.
Set a=-1. Set b = 1.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the quadratic function.
Exercise 16
Perform the following quadratic function transformation:
Reflection over the y-axis.
New function: y = (-x)2 , denoted by function f.
Set a=1. Set b= -1.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the quadratic function.
Exercise 17
Repeat this exercise as many times as desired until concept is mastered.
Use different values of a, b, h and k.