I think the basketball will go in because it will follow the slope of the graph. This is a quadratic function that models an equation which matches the arc of the basketball. Factors that play into the ball going into the hoop would be: gravity, wind, the snap of the thrower's wrist, etc.
-My predictions were very close for 21 inches and 14 inches, but not very close for the 7 inch ramp. My 7 inch graph was so different because I thought the skateboard would go further in the same amount of time, but it didn't. My initial reasoning for the shape of these graphs was that I thought the incline would be fast and the decline would be slightly slower.
-The zeroes of my graph represented the start and end points.
-The three graphs were different when talking about zeroes, maximums, and minimums. The maximums got lower with each graph, and the minimums got higher. The first zero was 0 for each one because that's where it started. The last zero was different for each one because each trial ended at a different point.
-The slope is highest for the 21 inch ramp because the ramp was tallest, and therefore gave the skateboard the most speed. The slope of the 14 inch ramp was slightly lower seems the ramp was also lower. The slope for the 7 inch ramp was the lowest of the three because the height was the lowest, giving the skateboard less speed. It's rising the fastest from 0-10/15 seconds and falling from 10/15-17/35 seconds.
Graph (A) would mean that he is raising the flag at a consistent speed, not speeding up or slowing down. Graph (B) would mean that he started out raising it fast, but then slowed down at the end, almost plateauing. Graph (C) would mean that he is constantly speeding up and slowing down, speeding up and slowing down, but at the same rate. Graph (D) would mean that he starts out slow, and then speeds up at the end. Graph (E) would mean that he starts slow, increases speed very quickly, and then slows down at the end. Graph (F) would (be nearly impossibly) mean the he raises the flag the height of the whole pole instantly.
I think that Graph (D) shows the most realistic situation because I think you would start out slow, then speed up when you get the hang of it.
I think that Graph (F) shows the most unrealistic situation because it is impossible to raise the flag instantly without any time passing.
In this piece of "art", there are a lot of things going on. There are 6 separate equations, as seen below, and each equations is technically 2 equations put together. For example, in the first equation the two parts are -6 =< y and y =< 6. The first half would form the line at -6 and then shade up, while the second half would form the line at 6 and shade down. The same happens with the second equation (-6 =< x =< 6), but instead it is formed horizontally. For the last four, the equations are also two smashed into one. Again, -x =< y and y =< x. The first draws a line at -1x and shades down, while the second draws a line at 1x and shades upwards forming a triangle. This is true for the other three quadrants. Put them all together and you get a picture that slightly resembles the British flag.