Quadratic Functions Transformations

Explore how different transformations affect the properties of quadratic functions. Enter a quadratic function, select a transformation, and see both graphs plotted. Then analyze the algebra corresponding to the selected transformation and then the properties such as the vertex, x-intercepts, y-intecrcepts, opening up or down, shift left or right, up or down ,. etc.

This app can be used in several interactive activities that can help gain deeper understanding of quadratic functions.

Enter quadratic function f(x):

f(x) =

Select transformation:

Transformed function h(x):

h(x) =

Understanding Quadratic Transformations

This interactive tool demonstrates various transformations of quadratic functions:

-f(x): Reflects the graph vertically (across the x-axis)
f(-x): Reflects the graph horizontally (across the y-axis)
-f(-x): Reflects the graph through the origin
|f(x)|: Takes the absolute value of the function
f(|x|): Takes the absolute value of the input
f(x/2): Horizontally stretches the graph by factor 2
f(2x): Horizontally compresses the graph by factor 1/2