Shot #1 (Let S Work Through This One Together)

Shot #1 (let’s work through this one together)

1.  Watch the video. I’ll play it for you. (If you’re looking at it later, here’s the video. You may have to try it a couple of times to get it to play, plus it’s very short. If it won’t play in your browser, try downloading and opening it.)

2.  What do you wonder?

3.  Open up this Desmos Graph.

4.  The flight of the basketball is parabolic (quadratic). Estimate where the vertex is. Put the appropriate numbers in for ‘h’ and ‘k’.

5.  What do you know must be true about the value of ‘a’? Experiment a bit with different values of ‘a’ to try to get the graph of the parabola to match the flight of the basketball.

6.  You’ve probably found that you can get fairly close to matching the path, but perhaps not as close as you’d like to predict the outcome. We’ll use some features of Desmos to try to get more precise values.

a.  First we can get more precise values in the slider for a, h and k. Click on the minimum value on the ‘a’ slider (should be -3 to start out). By this point you should know that the value of ‘a’ is somewhere between -0.1 and -0.4. So let’s set those as our upper and lower limits. Set 0.001 as the step value.

b.  Now we’ll do the same thing for ‘h’ and ‘k’. You should hopefully have a value of ‘h’ between 5 and 5.5, and a value of ‘k’ between 5 and 5.5. Enter those in as your lower and upper limits for both ‘h’ and ‘k’. Set 0.001 as the step value.

c.  These changes should allow you to change the values of a, h and k to the thousandth’s place. You can also zoom in on the graph itself, using the scroll wheel on your mouse if you have one, or using the + button in the upper right on Desmos. Try changing those values to come up with a more accurate equation that matches the path of the basketball even better than before.

7.  Predict whether he makes shot #1.

8.  Record your values of a, h and k, and your prediction on the sheet provided.

9.  Now we’ll look at it as a class and see if we were right.

Shot #2

1.  Repeat the steps above, except for the following modifications:

a.  Watch this video.

b.  Open up this Desmos Graph.

c.  Your values for the lower and upper limits for ‘a’, ‘h’, and ‘k’ in step 6 may (or may not) be different than for shot #1. Adjust accordingly.

d.  Record your values of a, h and k, and your prediction on the sheet provided.

2.  We’ll look at it as a class and see if we were right.

Shot #3

●  Video

●  Graph

Shot #4

●  Video

●  Graph

Shot #5

●  Video

●  Graph

Shot #6

●  Video

●  Graph

Shot #7

●  Video

●  Graph

This activity is the work of Karl Fisch, based on the work of Dan Meyer.