Systems

Functions

Linear Models

Systems Review

Thank you to fellow teacher Andrew Busch for sharing your awesomeness!

Here are 10 time-lapse photos of people being awesome while someone with a camera is freezing:

## SECTION 1:

1) Choose 2 of the pictures of skiers in Section 1.
2) Click on either the heading or the picture to go to the attached Desmos file.
3) Using the sliders, find ‘a’, ‘h’, and ‘k’ values to fit a quadratic equation onto the skier/snowboarder’s path while they are in the air.

4) Describe how you got your function to match the path of the athlete.
5) What relationships can you find between the graph and your ‘a’, ‘h’, and ‘k’ values?

## SECTION 2:

 1) Choose 2 pictures of skiers/snowboarders from section 2. 2) Click on either the heading or the picture to go to the attached Desmos file. 3) Describe what happens to the graph as the a-value gets larger? What about when ‘a’ is negative? 4) How does the graph change when you change the h-value? Be specific. 5) How does the graph change when you change the k-value? Be specific. 6) Given a graph, how would you find the values for ‘h’ and ‘k’ without sliders?

## SECTION 3:

 1) Now, only choose 1 of the pictures of snowboarders from section 3. 2) Click on either the heading or the picture to go to the attached Desmos file. 3) This time there will be one difference between these pictures and the previous section–I will have the vertex point plotted on the graph. 4) Revisit your explanation to #6 in section 2: “Given a graph, how would you find the values for ‘h’ and ‘k’ without sliders?” How would you change your explanation (if at all)? 5) After you find the ‘h’ and ‘k’ values for a graph, how can you find the ‘a’ value?