document.write( "Question 732251: A ball is tossed upward with an initial velocity of 122 ft/s from a platform that is 700 ft above the surface of the earth. After t seconds, the height of the ball above the ground is given by the equation h = -16t^2 + 122t + 700. What is the maximum height of the ball? Round to the nearest tenth of a foot. \n" ); document.write( "

Algebra.Com's Answer #852849 by ikleyn(53427) $\"\"$ $\"About$

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\n" ); document.write( "A ball is tossed upward with an initial velocity of 122 ft/s from a platform that is 700 ft above
\n" ); document.write( "the surface of the earth. After t seconds, the height of the ball above the ground is given
\n" ); document.write( "by the equation h = -16t^2 + 122t + 700. What is the maximum height of the ball?
\n" ); document.write( "Round to the nearest tenth of a foot.
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document.write( "This given equation  h = -16t^2 + 122t + 700  has the leading coefficient negative, -16.\r\n" );
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document.write( "So, it describes a parabola opened downward. Such a parabola has a maximum.\r\n" );
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document.write( "According to the general theory, a parabola y = ax^2 + bx + c with a negative leading coefficient 'a'\r\n" );
document.write( "has a maximum at the point  x = .  In our case, the maximum is achieved at\r\n" );
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document.write( "    x =  =  = 3.8125.\r\n" );
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document.write( "It means that the maximum height is achieved at 3.8125 second after tossing.\r\n" );
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document.write( "To find the maximum height h, substitute x = 3.8125 into the formula and calculate\r\n" );
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document.write( "    h = -16*3.8125^2 + 122*3.8125 + 700 = 932.6 feet (rounded as requested).\r\n" );
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document.write( "ANSWER.  The maximum height of the ball is 932.6 feet.\r\n" );
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