document.write( "Question 1099516: An object is thrown straight up into the air then follows a trajectory , the height s(t)of the object is given by the function s(t)=4t-16t²
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Algebra.Com's Answer #713944 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "It is about finding the vertex (the maximum) of the quadratic function\r\n" );
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document.write( "s(t) = -16*t^2 + 4t.\r\n" );
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document.write( "In the given case you can present the function as the product\r\n" );
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document.write( "s(t) = -4t*(4t-1)\r\n" );
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document.write( "of two factors -4t and (4t-1). Then it is clear that the quadratic function has the roots at t = 0  and t = 1/4.\r\n" );
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document.write( "Then the midpoint t = 1/8 is the point where the quadratic function reaches its maximum.\r\n" );
document.write( "So the time to get maximum height is 1/8 of a second.\r\n" );
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document.write( "Then the maximum height is   =  = .\r\n" );
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document.write( "Answer.  The maximum height is  of the foot and it reaches at t = 1/8 of a second.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Plot h(t) = $\"-16%2At%5E2+%2B+4t\"$ \r
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\n" ); document.write( "\n" ); document.write( "There is another way to analyze the problem.\r
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\n" ); document.write( "\n" ); document.write( "It is described in lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on an arrow shot vertically upward\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a ball thrown vertically up from the top of a tower \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "In any case, you need to know how to find the maximum/minimum of a quadratic function presented in the general form.\r
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\n" ); document.write( "\n" ); document.write( "You will find it in the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
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