Copy of 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(x - h)2 +k
Note: The 'slider' feature on the x-y coordinate plane can be used to change the a, 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:
The new function is y=x2 + 3 , denoted by function f(x).
Find the the vertex of f(x).
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 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 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 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 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 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 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 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 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 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 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 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:
Reflection over the x-axis.
New function: y = - x2 , denoted by function f.
Set a=-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 14
Discuss the effect of different values of a, h and k on the graph of .
Reflection
How well did you understand the math in this lesson?
How did you feel about this lesson?
Reflect on the math from this lesson.