document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090463>Question 1090463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation y = -16t^2 - 18t + 405 describes the height (in feet) of a ball thrown downward at 18 feet per second from a height of 405 feet from the ground. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest tenth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704908 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>When the ball hits the ground, its height is 0.  So you want to solve the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2-18t%2B405=0 ALIGN=MIDDLE  ALT=\"-16t%5E2-18t%2B405=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The question asks for an answer to the nearest tenth, suggesting that the answer is not a \"nice\" number and has to be rounded.  However, the quadratic expression factors, yielding an exact answer.<br><BR>\n" );
document.write( "You could just use the quadratic formula, or perhaps a graphing calculator or some other such tool, to find the answer.  But let's instead get some practice with this problem on factoring quadratics.<br><BR>\n" );
document.write( "I would first factor out a -1, so that the leading coefficient is positive; factoring a quadratic with a negative leading coefficient I find to be a very unpleasant task.  So our quadratic is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2816t%5E2%2B18t-405%29 ALIGN=MIDDLE  ALT=\"-1%2816t%5E2%2B18t-405%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "With a leading coefficient of 16, the leading coefficients of our two binomial factors could be 1 and 16, or 2 and 8, or 4 and 4.<br><BR>\n" );
document.write( "But in fact they can't be 4 and 4 -- because then the coefficient of the linear (x) term would have to be a multiple of 4, which it is not.<br><BR>\n" );
document.write( "And leading coefficients of 1 and 16 on the binomial factors is unlikely, so I would look first for a factorization with 2 and 8 as the leading coefficients of the two binomial factors.<br><BR>\n" );
document.write( "Some of the possible factorizations of the constant term 405 are 81*5, 27*15, 9*45, ....  Some playing around with the different possible combinations shows the factorization to be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2%2B18r-405=%288t%2B45%29%282t-9%29 ALIGN=MIDDLE  ALT=\"16t%5E2%2B18r-405=%288t%2B45%29%282t-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Setting the first factor equal to 0 gives us a negative value for the time t, which does not make sense in the actual problem.  Setting the second factor equal to 0 gives us the value of 4.5 for t.<br><BR>\n" );
document.write( "So that is the answer to the problem: the ball hits the ground after 4.5 seconds.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );