Algebra.Com's Answer #840800 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "A soccer ball is kicked off the ground into the air and reaches its maximum height after 2 seconds.
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document.write( "After 1 second the height of the ball is 15 feet off the ground.
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document.write( "Write a quadratic equation in vertex form to model this situation.
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document.write( "They want you find a quadratic equation in vertex form\r\n" );
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document.write( " h(t) =  . (1)\r\n" );
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document.write( "It is the general quadratic equation in vertex form.\r\n" );
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document.write( "Now, the problem says that the ball reaches its maximum height after 2 seconds.\r\n" );
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document.write( "It means that the vertex is at t=  ; in other words, we should take = 2 (seconds).\r\n" );
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document.write( "So, I write \r\n" );
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document.write( " h(t) =  . (2)\r\n" );
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document.write( "Next, the problem says that After 1 second the height of the ball is 15 feet off the ground.\r\n" );
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document.write( "It means that I can write the last equation (2) in the form\r\n" );
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document.write( " 15 =  , (3)\r\n" );
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document.write( "substituting 15 ft on the left side and replacing \"t\" by 1 second in the right side.\r\n" );
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document.write( "It gives me \r\n" );
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document.write( " 15 = a + b. (4)\r\n" );
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document.write( "Finally, the problem says that the ball is kicked off the ground.\r\n" );
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document.write( "It means that at t= 0 the height is zero: h = 0.\r\n" );
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document.write( "So, I substitute t= 0 and h= 0 into equation (2), and I get then\r\n" );
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document.write( " 0 =  ,\r\n" );
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document.write( "or\r\n" );
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document.write( " 0 = 4a + b. (5)\r\n" );
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document.write( "From (5), I have b = -4a and substitute it into equation (4). I get then\r\n" );
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document.write( " 15 = a + (-4a) = -3a;\r\n" );
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document.write( "hence\r\n" );
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document.write( " a =  , or a = -5.\r\n" );
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document.write( "Now I am ready to write the final equation from given data\r\n" );
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document.write( " h(t) =  . <<<---===  \r\n" );
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document.write( " | But now it is good time to discuss it. |\r\n" );
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document.write( "First, having this equation in front of you, you can check that it SATISFIES the problem's conditions.\r\n" );
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document.write( "Second, it is good to re-write this equation in the standard form quadratic equation by opening parentheses\r\n" );
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document.write( " h(t) = -5*t^2 + 10t + 0. (6)\r\n" );
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document.write( "The zero (0) as a constant term is good, because it tells that the initial height is zero at t= 0.\r\n" );
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document.write( "Next, from the standard form (6) everybody, who is familiar with the subject, will say\r\n" );
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document.write( " \"HEY, they missed everything in the problem: the leading coefficient a= -5 says that the problem \r\n" );
document.write( " should consider METERS instead of FEET. For the Earth condition, a= -5 tells that the input numbers\r\n" );
document.write( " in the condition relate to METERS, not feet\".\r\n" );
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document.write( "At this point, I complete my solution and my explanations.\r\n" );
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document.write( "From my post, you learn TWO THINGS:\r\n" );
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document.write( " - first, you learn on HOW TO analyze and solve the problem, step-by-step.\r\n" );
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document.write( " - second, you learn that the problem's formulation, as it is given in the post,\r\n" );
document.write( " is INCOORRECT and the word \"feet\" MUST BE replaced by the word \"METERS\" there.\r\n" );
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document.write( "Solved and COMPLETED.\r
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document.write( "You should not be surprised by the error in the condition:
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document.write( "at this forum, every second post struggles having ERRORS, fatal or not-fatal.\r
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