In our Ch. 0 Graphing Functions Project, we illustrated the different transformation graphs of five different functions.

1. The original parent function is y = x

^{2}.

2. The vertical translation, with a function of y = x

^{2}- 3, is shown in blue. I moved the parent function down 3 units.

3. The horizontal translation, with a function of y= (x - 3)

^{2 }, is shown in red. I moved the parent function 3 units to the right.

4. The vertical + horizontal translation, with a function of y = (x - 3)

^{2 }- 3, is shown in purple. I moved the parent function 3 units to the right and 3 units down.

5. The horizontal reflection, with a function of y = (-x)

^{2}, is shown in pink. I flipped the parent function graph across the x-axis.

6. The vertical reflection, with a function of y = -x

^{2}, is shown in green. I flipped the parent function graph across the y-axis. Also, since the parent function and the horizontal reflection would equal the same, they have the same graph.

7. The vertical + horizontal translation + vertical reflection, which a function of y = | x - 3 | - 3, is shown in orange. I flipped the vertical + horizontal translation function (purple) across the y-axis.