What these graphs show is my prediction (light blue) of what the graph would look like when we let go of a skateboard from a ramp that was 21in, 14in, and 7in high. At the end of the ramp was a sloped driveway that was measured to 64in. The dots are the actual points of the skateboard as it traveled down the driveway.
My first prediction wasn't close to the actual measurements at all. As the graphs went on I was more accurate with my predictions. What made then less accurate was that I didn't estimate the time as the skateboard fell down the ramp and down the driveway. I made my first estimate time to long to reach its maximum but the rest were better. I knew that the skateboard would reach a maximum bu then would come back down due to the sloped driveway. With this information I was able to come up with a graph. The domain of my first two graphs are [0,37] and for the last graph on the right it was [0,16] The range for my first graph (on the left) was [0,66]. The middle graph's range was [0,55]. The range for the last graph was [0,43]. Each graph had a minimum of zero. Even though they all had the same minimum, they all had different maximums. The maximum for 21in ramp was the highest and as the ramp moved down from 21in to 14in to 7in the maximum decreased with it. The graph rises the fastest when the skateboard hits the driveway because of the speed its gained. It starts to slow when it hits the maximum and rolls backwards on the driveway while decreasing speed. It falls the fastest when it hits it's maximum but then it decreases speed as it continues to roll. The less steep the graph the slower the skateboard is moving.
My first prediction wasn't close to the actual measurements at all. As the graphs went on I was more accurate with my predictions. What made then less accurate was that I didn't estimate the time as the skateboard fell down the ramp and down the driveway. I made my first estimate time to long to reach its maximum but the rest were better. I knew that the skateboard would reach a maximum bu then would come back down due to the sloped driveway. With this information I was able to come up with a graph. The domain of my first two graphs are [0,37] and for the last graph on the right it was [0,16] The range for my first graph (on the left) was [0,66]. The middle graph's range was [0,55]. The range for the last graph was [0,43]. Each graph had a minimum of zero. Even though they all had the same minimum, they all had different maximums. The maximum for 21in ramp was the highest and as the ramp moved down from 21in to 14in to 7in the maximum decreased with it. The graph rises the fastest when the skateboard hits the driveway because of the speed its gained. It starts to slow when it hits the maximum and rolls backwards on the driveway while decreasing speed. It falls the fastest when it hits it's maximum but then it decreases speed as it continues to roll. The less steep the graph the slower the skateboard is moving.