1. Unit 2.2
Quadratic Functions

2. Example 1

3. How would you describe the motion?
What quantities are being observed and how they are changing over time?
What is the change of elevation of the ball over time?

4. How would you describe the motion?
What quantities are being observed and how they are changing over time?
Elevation vs. time, they are decreasing
What is the change of elevation of the ball over time?
Speeds up at the bottom of the ramp

5. Story Graphs Graph the Story: Questions:
What would the labels and units of the axes be?
What would you title this graph?
What was the height of the ball at 0 seconds?
What is the meaning for a point plotted on the graph?
How long did it take for the ball to roll down the ramp?
What happened to the ball at the end of the ramp?

6. Story Graphs Graph the Story: Questions:
What would the labels and units of the axes be?
Elevation (inches), Time (seconds)
What would you title this graph?
Elevation vs. time of a ball rolling down an
incline
What was the height of the ball at 0 seconds?
12 inches
What is the meaning for a point plotted on the graph?
Elevation of the ball at a certain time
How long did it take for the ball to roll down the ramp?
About 2 seconds
What happened to the ball at the end of the ramp?
It rolled across the floor

7. graph of Ball Rowling down an incline
Is the change in elevation faster at different times?
Should the line be curved or straight? Why?

8. graph of Ball Rowling down an incline
Is the change in elevation faster at different times?
Yes, faster at the bottom of the ramp.
Should the line be curved or straight? Why?
Curved because if it was straight it would mean the rate of change
would be constant as it rolled down the board, which it is not.

9. Example 2: world record shallow dive
What would the labels and units of the axes be?
What would you title this graph?
How high is the diver at the top of the ladder?
Does his elevation ever increase?
How long does it take for the diver to reach the pool?

10. Example 2: world record shallow dive
What would the labels and units of the axes be?
y axis: Elevation (feet), x axis: Time (seconds)
What would you title this graph?
Elevation vs. Time World Record Shallow Dive
How high is the diver at the top of the ladder?
Thirty-five feet
Does his elevation ever increase?
Yes, at the very top of the dive, he jumps up.
How long does it take for the diver to reach the pool?
Approximately 1.5 seconds

11. Example 2: world record shallow dive
How does your graph compare?

12. Example 3: graphing a quadratic equation from a table
The table below gives the area of a square with sides of whole number lengths.
Plot the following points on a graph.
What goes on the Y axis, X axis? Why?

13. Example 3: graphing a quadratic equation from a table
The coordinates are (0,0) (1,1) (2,4) (3,9) (4,16) (5,?)

14. Example 3: graphing a quadratic equation from a table
The coordinates are (0,0) (1,1) (2,4) (3,9) (4,16) (5,25)

15. Example 3: graphing a quadratic equation from a table
What would reflecting the graph across the y axis look like?

16. Example 3: graphing a quadratic equation from a table
What would reflecting the graph across the y axis look like? (0,0) (-1,-1) (-2,4,) (-3,9) (-4,16) (-5,?) “Quadratic Equation”

17. Example 3: graphing a quadratic equation from a table
On the graph, what do the points between the plotted points from the table represent?

18. Example 3: graphing a quadratic equation from a table
On the graph, what do the points between the plotted points from the table represent? They represent the areas of square with non-whole number side lengths.

19. Exit Ticket
If you jumped in the air three times, what might the elevation versus time graph of that story look like?
Label the axes appropriately.

20. Exit Ticket
If you jumped in the air three times, what might the elevation versus time graph of that story look like?
Label the axes appropriately.