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# Tracking a Ball

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Lesson for St. Matthews School

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### Tracking a Ball

1. 1. 35 20 17 28 21 25 10 7 18 11 38 23 20 31 24 29 14 11 22 15 27 12 9 20 13
2. 2. Why does it work? e d c b a j i h g f + 35 20 17 28 21 12 25 10 7 18 11 2 38 23 20 31 24 15 29 14 11 22 15 6 27 12 9 20 13 4 23 8 5 16 9 +
3. 3. 4.1 Tracking a Ball Time (sec) Height (feet) 0 4.00 15 3.75 28 3.50 39 3.25 48 3.00 55 2.75 60 2.50 63 2.25 64 2.00 63 1.75 60 1.50 55 1.25 48 1.00 39 0.75 28 0.50 15 0.25 0 0.00 Height (feet) Time (Seconds)
4. 4. <ul><li>1. Use the table to describe the height of the ball over this 4 second time period. </li></ul><ul><li>2. Make a graph. Describe as many important features as you can. </li></ul><ul><li>3. Does the graph represent a quadratic function? Explain. </li></ul>B. The height h of the ball in feet after t seconds is given by the equation: h = - 16 t 2 + 64 t 1. Graph this equation on your calculator and sketch the graph. Window Xmin=0 Xmax=5 Xscl=1 Ymin=0 Ymax=80Yscl=10
5. 5. <ul><li>Does this graph match the graph that you plotted? Explain. </li></ul><ul><li>Use the graph to predict when the ball will reach a height of 58 feet? Explain. </li></ul><ul><li>Use the equation to calculate the height of the ball after 1.6 seconds. </li></ul><ul><li>When will the ball hit the ground? Explain. </li></ul><ul><li>Factor the equation. Use the factored form to predict the x-intercepts. </li></ul>
6. 6. <ul><li>Complete the table of values. Use a pattern to save time. </li></ul><ul><li>Plot on the same coordinate plane as before. </li></ul><ul><li>Check your graphs by graphing both equations on your calculator. Sketch the result. </li></ul><ul><li>Compare the two graphs by discussing maximum height, x and y intercepts, and patterns of change. </li></ul>4.00 3.75 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 Height (feet) Time (Seconds)
7. 7. Frog 4.2 Comparing Quadratic Relationships Flea A. 1. Complete each table of values and plot all 3 on the same graph. Be sure to label each graph. Basketball Player 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Height (feet) Time (Seconds) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Height (feet) Time (Seconds) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Height (feet) Time (Seconds)
8. 8. Time Height
9. 9. <ul><li>Graph each equation on your calculator and sketch each graph to check your plotted graphs. You may graph all 3 at the same time. </li></ul><ul><li>Use the graphs to complete the chart. </li></ul>4. What do the constant terms 0.2 and 6.5 tell you about the frog and basketball player? Why does the flea not have a constant? Basket Ball Player Flea Frog Length of Time that Jump Lasted Time that Maximum Height was Reached Maximum Height Reached