1. The original parent function of this graph was y=|x|
2. Then, I wanted to do a vertical translation 8 units up, which led me to get the equation of y=|x|+8. As you can see, this function was in red and the vertex moved 8 units up on the y-axis.
3. Next, to do a horizontal translation, I decided that I wanted to move the graph 8 units to the right along on x-axis, so the equation became y=|x-8|, the function is shown in blue.
4. After that, I wanted to do a reflection across the x-axis, so my equation was y = -|x|, which was shown in purple. All of my y point from my (x,y) coordinates had become negative.
5. In green, I had done a horizontal translation 2 units to the left, followed by a vertical translation 4 units down(y=|x+2|-4.
6. Finally, for my last black graph, equation I had reflected my original function across the x-axis and then did a vertical translation 10 units down. The equation i ended up with was y= -|x-3|-10.
For Back to School Night, I brought my mom. She laughed at the idea of me teaching her Math, because she had barely been able to get a decent education growing up. As the night proceeded and as she began trying the translations it made a little more sense to her. She got the idea of doing vertical translations and horizontal translations.