document.write( "Question 1175897: A person standing close to the edge on top of a 112-foot building throws a ball vertically upward. The quadratic function h(t) = −16t^2 + 96t + 112 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.\r
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Algebra.Com's Answer #801681 by ikleyn(52777) $\"\"$ $\"About$

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\n" ); document.write( "A person standing close to the edge on top of a 112-foot building throws a ball vertically upward.
\n" ); document.write( "The quadratic function h(t) = −16t^2 + 96t + 112 models the ball's height about the ground, h(t), in feet,
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\n" ); document.write( "a) What is the maximum height of the ball?
\n" ); document.write( "(Round your answer to the nearest hundredths.)\r
\n" ); document.write( "\n" ); document.write( "b) How many seconds does it take until the ball hits the ground?
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\n" ); document.write( "\n" ); document.write( " Part (a)\r
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document.write( "To find the maximum height, you first find the time to get maximum height\r\n" );
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document.write( "      t =  -   = -  =  = 3 second.\r\n" );
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document.write( "Then the maximum height is the given function t(t) at t= 3 seconds\r\n" );
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document.write( "    h(3) = -16*3^2 + 96*3 + 112 = 256 feet.     ANSWER\r\n" );
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document.write( "To find the time when the ball hits the ground, you solve this equation\r\n" );
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document.write( "    h(t) = 0,  which is  -16t^2 + 96t + 112 = 0.\r\n" );
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document.write( "To simplify, divide both sides bu -16\r\n" );
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document.write( "    t^2 - 6t - 7 = 0\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (t-7)*(t+1) = 0.\r\n" );
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document.write( "Two roots of the quadratic equation are t= 7 and t= -1;\r\n" );
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document.write( "Only positive value  t= 7 is the solution.\r\n" );
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document.write( "The ball hits the ground in 7 seconds.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems, slook into 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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\n" ); document.write( "\n" ); document.write( "On finding the maximum/minimum of a quadratic function, learn from 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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