In math functions, we can see certain pieces of functions changing a function in particular ways. To begin, you first have to know about parent functions. These are the plain functions that have not been changed at all. The parent function for a quadratic function is shown below.

The most basic transformation of all transformation is a simple vertical shift. We do this by simply adding something to the end of the function. The graph below shows a shift of 5 up.

Similar to the vertical shift, the horizontal shift is done by adding or subtracting something to the function. The difference in the shift horizontally is that it is done to the input of the function rather than the output. Because this is done to the input, the shift goes in the opposite direction that you may anticipate.

From the basic transformations above, we will go to more complicated versions below. The graph below shows a vertical compression and a vertical reflection.

Using the basic ideas above, play with the graph below to see how the function changes as the different parameters change.