Algebra.Com's Answer #645108 by KMST(5328)![\"\"](\"/images/stars/stars-13.gif\")  
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The diver's height,  (in feet), above the water can be modeled by
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document.write( " for  ,
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document.write( "where  is the time since the diver jumped off the diving board, and
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document.write( " is the total time (in seconds) that the diver is in the air.
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document.write( "Negative times make no sense, because the model equation/function cannot predict how high above the water the diver was at various times before jumping off the board.
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document.write( "Times after the diver hits the water make no sense either. The model will not work for those times.
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document.write( "(a) The diver hits the water at  , when the diver's height, (in feet), above the water is
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document.write( " , so
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document.write( "To solve that quadratic equation we could
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document.write( "use the quadratic formula, or
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document.write( "factor the quadratic polynomial, or
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document.write( "\"complete the square\".
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document.write( "FACTORING:
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document.write( "We notice that  can be factored many ways,
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document.write( "but one of them,  , has factors that add to the middle coefficient:
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document.write( " .
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document.write( "So we re-write the polynomial (and the equation) as
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document.write( " , and factor by parts:
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document.write( "--> --> .
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document.write( "The solutions to that equation,
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document.write( "coming from 
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document.write( "are  and  .
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document.write( "Since the function was defined for a domain of  ,
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document.write( "the only solution that makes sense is  .
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document.write( "The diver is in the air for  seconds.
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document.write( "COMPLETING THE SQUARE:
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document.write( "--> --> --> --> --> .
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document.write( "So, either  or  .
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document.write( " --> --> --> .
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document.write( "The other choice,  , yields a negative value for ,
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document.write( "which is not in the domain where the model function should be defined,
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document.write( "and it would not make sense to say that the diver is in the air for a negative number of seconds after jumping off the board.
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document.write( "(b) is a quadratic function with the negative leading coefficient  .
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document.write( "APPLYING FORMULAS:
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document.write( "A formula that your teacher may have wanted to make you memorize says that a quadratic function
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document.write( " with a negative leading coefficient,  ,
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document.write( "has a maximum for  .
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document.write( "In this case, we have instead of  , and  instead of  .
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document.write( "Then, we have  , and  .
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document.write( "So, the maximum height happens at  .
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document.write( "At that time, the height is
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document.write( " .
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document.write( "JUST USING YOUR AWESOME KNOWLEDGE OF BASIC ALGEBRA, BECAUSE YOU'D RATHER REASON THAN MEMORIZE AND APPLY FORMULAS:
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document.write( "Since  ,  ,
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document.write( "and  only when  <--> .
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document.write( "Either way you can get to the answer,
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document.write( "the maximum height is  feet, and it occurs after  seconds. \n" );
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