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7.3 Quadratic Patterns

7.3 Quadratic Patterns
  • Math Help

    In Example 5, the ratios of consecutive terms are not equal.

    So, the pattern is not exponential.

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  • Checkpoint Solution

    Rewrite the table using 1-second intervals. Each first difference tells you how much the distance increased during 1 second, or the speed of the shot put ball. Each second difference tells you how much the speed of the shot put ball increased during 1 second.

    First differences: changes in distance

    Second differences: changes in speed

    As you can see, the speed is increasing by 32 feet per second each second. You can summarize this information in a table. (Note that at 0 seconds, the speed is 0 feet per second because you have not dropped the ball yet.)

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      _____     ______    _____     _____     _____   
     /  ___||  /_   _//  |__  //   |  ___||  / ____|| 
    | // __     -| ||-     / //    | ||__   / //---`' 
    | \\_\ ||   _| ||_    / //__   | ||__   \ \\___   
     \____//   /_____//  /_____||  |_____||  \_____|| 
      `---`    `-----`   `-----`   `-----`    `----`  
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