document.write( "Question 1149032: a fastball is hit straight up over home plate. the balls height, H( in feet), from the ground is modeled by the quadratic function defined by H(t)=16^t2+80t+5 where t is measured in seconds. at what time did the fastball reach the maximum height? solve algebraically \n" ); document.write( "

Algebra.Com's Answer #770364 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a fastball is hit straight up over home plate. the balls height, H( in feet), from the ground is modeled
\n" ); document.write( "by the quadratic function defined by H(t)=16^t2+80t+5 where t is measured in seconds.
\n" ); document.write( "at what time did the fastball reach the maximum height? solve algebraically
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\n" ); document.write( "\n" ); document.write( "            First, the function H(t) in your post is written INCORRECTLY, having a FATAL error.\r
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\n" ); document.write( "\n" ); document.write( "            The correct form of this function is H(t) = -16t^2 + 80t + 5.\r
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\n" ); document.write( "\n" ); document.write( "            Notice the sign \" - \" (minus) before 16t^2   (!)\r
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\n" ); document.write( "\n" ); document.write( "            With the corrected formula, see my solution below.\r
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document.write( "The function  H(t) = -16t^2 + 80t + 5  is a quadratic function, whose plot is a parabola opened down.\r\n" );
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document.write( "This quadratic function has the maximum at the value of its argument  t = , where \"a\" is the coefficient at t^2\r\n" );
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document.write( "and \"b\" is the coefficient at t.\r\n" );
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document.write( "In your case, a= -16,  b= 80, so the function gets the maximum at  t =  = 3.5.\r\n" );
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document.write( "So, the fastball gets the maximum height  2.5 seconds after is hit straight up. ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function, see 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
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "On solving similar problems to yours in this post, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on a projectile moving vertically up and down\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( "    - Problem on a toy rocket launched vertically up from a tall platform\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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