Transforming graphs of functions is something that can be done in Math. Where we already have the graph of a function, but can apply operations to the function in order to change the location or shape of the graph.
This page will show examples of transformations that can be done to a quadratic graph, and the operations that create them.
The quadratic graph we’ll use is a standard curve shown below, but the transformations shown on this page do also apply to other quadratic graphs that can be encountered.
![Standard Graph.](http://www.learnermath.com/wp-content/uploads/2023/09/standard-quadratic-graph.png)
Transforming Graphs Examples
1) y = \space {\text{-}}f(x)
Reflect the graph in the x-axis.
![Graph reflected in the x axis.](http://www.learnermath.com/wp-content/uploads/2023/09/reflected-x-axis.png)
2) y = \space f({\text{-}}x)
Reflect the graph in the y-axis.
![Graph reflected in the y axis.](http://www.learnermath.com/wp-content/uploads/2023/09/reflected-y-axis.png)
3) y = \space {\text{-}}f({\text{-}}x)
Reflect the graph in the y-axis, then the x-axis.
![An example of transforming graphs in Algebra.](http://www.learnermath.com/wp-content/uploads/2023/09/transforming-graphs.png)
4) y = \space f(x) + 1
Move the graph up the x-axis 1 unit.
![Graph moved up the x axis one unit.](http://www.learnermath.com/wp-content/uploads/2023/09/up-1-unit.png)
5) y = \space f(x + 1)
Move the graph along the y-axis 1 unit left.
![Graph moved left along the y axis one unit.](http://www.learnermath.com/wp-content/uploads/2023/09/1-unit-left.png)
6) y = \space f(\frac{x}{2})
Stretch the graph by 2 in the x direction.
![Graph stretched by 2 in the x direction.](http://www.learnermath.com/wp-content/uploads/2023/09/stretch-x-axis.png)
7) y = \space 2f(x)
Stretch the graph by 2 in the y direction.
![Graph stretched by 2 in the y direction.](http://www.learnermath.com/wp-content/uploads/2023/09/stretch-y-axis.png)
8) y = \space 2 \space {\text{--}} \space f(x)
Reflect the graph in the x-axis, then move up by 2 units.
![Graph reflected in the x axis, then moved up 2 units.](http://www.learnermath.com/wp-content/uploads/2023/09/reflect-x-move-up.png)