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Model Quadratic Launch for Pumpkin Tossing Contest

Calculating the optimal launch angle for pumpkin tossing using quadratic regression model on a graphing calculator.

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Model Quadratic Launch for Pumpkin Tossing Contest

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  1. EXAMPLE 4 Solve a multi-step problem Pumpkin Tossing A pumpkin tossing contest is held each year in Morton, Illinois, where people compete to see whose catapult will send pumpkins the farthest. One catapult launches pumpkins from 25feet above the ground at a speed of 125 feet per second.

  2. EXAMPLE 4 Solve a multi-step problem The table shows the horizontal distances (in feet) the pumpkins travel when launched at different angles . Use a graphing calculator to find the best-fitting quadratic model for the data.

  3. EXAMPLE 4 Solve a multi-step problem SOLUTION STEP 1 STEP 2 Enter the data into two lists of a graphing calculator. Make a scatter plot of the data. Note that the points show a parabolic trend.

  4. EXAMPLE 4 Solve a multi-step problem STEP 3 STEP 4 Use the quadratic regression feature to find the best fitting quadratic model for the data. Check how well the model fits the data by graphing the model and the data in the same viewing window.

  5. EXAMPLE 4 Solve a multi-step problem ANSWER The best-fitting quadratic model is y = –0.261x2 + 22.6x + 23.0.

  6. ANSWER About 43°; the vertex of the graph gives what angle measure produces the greatest distance. for Example 4 GUIDED PRACTICE Pumpkin Tossing 7. In Example 4, at what angle does the pumpkin travel the farthest? Explain how you found your answer.

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