This year Addison Trail High School's conference record is 4-1! They are tied for first with Willowbrook High School (boo!) and need to win the championship game in order to take the conference title.
The teams are tied at one game apiece, and are currently in the third game. The score is 24-23 and Nick is about to serve. The path that the volleyball takes could determine if the team wins or loses! |
Source: http://www.clipartpanda.com/categories/volleyball-player-hitting-silhouette
As Nick begins to serve underhand, his wrist makes contact with the ball about 4 feet in the air. The ball sails toward the net with a parabolic path and the crowd watches in anticipation of the ball going over the net, Willowbrook missing the shot and Addison Trail winning the conference title!
Suppose the ball's motion is best described by a quadratic function. The equation
Suppose the ball's motion is best described by a quadratic function. The equation
models the data where t is the time in seconds and h(t) is the height of the ball in feet.
Answer the following questions!
Answer the following questions!
a.) If the height of the net is 8 feet, is it possible for the ball to make it over the net?
b.) If so, how long do the Willowbrook players have to return the ball before it hits the ground and Addison Trail wins?!
c.) When determining the equation of best fit, why do you think the volleyball team decided to use a quadratic equation? Do you think another function would have been more appropriate? Discuss other functions that could model this situation and the pros and cons of using these other equations.
d.) Consider other examples of parabolas in the world and create your own real life example of a quadratic equation! Throughout this process, identify a real life scenario and present a quadratic function that will model your situation. Then decide why you would use this model to find the vertex and the x-intercept in real life!
b.) If so, how long do the Willowbrook players have to return the ball before it hits the ground and Addison Trail wins?!
c.) When determining the equation of best fit, why do you think the volleyball team decided to use a quadratic equation? Do you think another function would have been more appropriate? Discuss other functions that could model this situation and the pros and cons of using these other equations.
d.) Consider other examples of parabolas in the world and create your own real life example of a quadratic equation! Throughout this process, identify a real life scenario and present a quadratic function that will model your situation. Then decide why you would use this model to find the vertex and the x-intercept in real life!