document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169617>Question 1169617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> H= -5t^2+20t models the height of a ball that is kicked into the air, where H is the ball's height in meters and t is time in seconds after being kicked.\r<BR>\n" );
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document.write( "a) How long is the ball in the air for?\r<BR>\n" );
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document.write( "b) When will the ball reach its maximum height?\r<BR>\n" );
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document.write( "c) What is the maximum height reached by the ball?\r<BR>\n" );
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document.write( "d) At what time(s) will the ball be 15 meters in the air? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794400 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height of the ball as a function of the time is represented by a parabola.<BR>\n" );
document.write( "The vertex of the parabola with equation y = ax^2 + bx + c, is at x = -b/2a.<BR>\n" );
document.write( "Thus, the time to reach maximum height = -20/-10 = 2 s. The ball is in the air for<BR>\n" );
document.write( "twice that, or t = 4 s.  <BR>\n" );
document.write( "The maximum height is given by H(2) = -5(2)^2 + 20(2) = -20 + 40 = 20 m<BR>\n" );
document.write( "15 = -5t^2 + 20t -> -5(t^2 - 4t + 3) = 0. This factors as (t-3)(t-1) = 0.<BR>\n" );
document.write( "Thus, there are two times when the ball is at 15 m, t = 1s and t = 3s. </SPAN>\n" );
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