Real-World Adventures with Representations Quadratic and Exponential functions

Activity- Bouncing a Ball When a ball goes through the air, what happens?

What would the graph look like? What is the dependent variable? What is the independent variable? Height (in meters) Time (in seconds)

Again, what does it look like?

What kind of graph represents the ball’s projection?  It’s not linear, that’s for sure.  Yes, can be represented by a quadratic  What is the general form of a quadratic? y = ax 2 + bx +c where y is the distance (m) and x is the time (s)

How do you determine the quadratic function from a graph?  What do we need to determine (find)?  Select three points from the graph, for this... -select the points throughout the curve, not within close proximity to each other  Plug the ordered pairs into the equation example of one point(4,2), 2= 16a +4b +c  Determine a, b, & c from Linear Combs, or Determinants(use the graphing calculator)

Bouncy Ball  When a ball bounces on the ground, does the ball reach the same height as the previous bounce?  What do you notice about any two successive bounces?  Is the amount of distance that it decreases, always the same?

Look at the height for each successive bounce(yes,again)- What are the independent and dependent variables?

Sketch a graph on your paper.

The number of bounces is the independent variable and the max height of of each bounce is the dependent variable

What kind of function do you think the height vs. number of the bounce represents?  How would you justify your conclusions?  Well, don’t just sit there. Determine if the following is an exponential function?

Now, its your turn!  Using the graphing calculator in conjunction with the CBL, record data for a ball bouncing  Work within a group of students (no more than 4)  Each individual will hand in his own report  Expectation on hand-outhand-out

Need a hint? ing_balls.html