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:
Set h=0
Set k=0
Slide a for different values.
What is the effect of a on the graph of f(x)?
Exercise 2
Perform the following quadratic function transformation:
Set 1=0
Set k=0
Slide h for different values.
What is the effect of h on the graph of f(x)?
Exercise 3
Perform the following quadratic function transformation:
Set a=0
Set h=0
Slide k for different values.
What is the effect of k on the graph of f(x)?
Exercise 4
Perform the following quadratic function transformation:
Set a=1
Set h=2
Set k=3
What the turning point of the graph of f(x)?
Exercise 5
Perform the Exercise 4 for some other values of a, h,and k.
What the turning point of the graph of y = a(x - h)2 +k?
Exercise 6
What is the other name for the turning point?
Exercise 7
A function is denoted by function f: y = (x + 3)2 - 4. Find the vertex of f(x).
Exercise 8
For a=1, write the quadratic function f(x) with the vertex (2,4).
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.