document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203132>Question 1203132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ship fires a distress flare up into the air.  The height (meters) and the time (seconds) are related by y = - 5 ( x - 2.5) ² + 75 \r<BR>\n" );
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document.write( "a.) What was the maximum height of the flare?\r<BR>\n" );
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document.write( "b.) At what time (in seconds) did the maximum height occur?\r<BR>\n" );
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document.write( "c.) At what height was the flare fired from the ship?\r<BR>\n" );
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document.write( "d.) When did the flare hit the water?<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 #838447 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A ship fires a distress flare up into the air. The height (meters) and the time (seconds) <BR>\n" );
document.write( "are related by y = - 5 ( x - 2.5) ² + 75\r<BR>\n" );
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document.write( "(a) What was the maximum height of the flare?\r<BR>\n" );
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document.write( "(b) At what time (in seconds) did the maximum height occur?\r<BR>\n" );
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document.write( "(c) At what height was the flare fired from the ship?\r<BR>\n" );
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document.write( "(d) When did the flare hit the water?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "The formula y = -5*(x-2.5)^2 + 75 represents a downward parabola,\r\n" );
document.write( "written in vertex form.\r\n" );
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document.write( "(a)  The maximum height is 75 meters\r\n" );
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document.write( "     (because some non-negative quantity 5*(x-2.5)^2 is subtracted from 75).\r\n" );
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document.write( "(b)  The maximum height of 75 meters occurs when x= 2.5 seconds, making the term  -5*(x-2.5)  equal to zero.\r\n" );
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document.write( "(c)  To answer this question, substitute x= 0 into the formula, which \r\n" );
document.write( "     represents the initial condition when the time counter started.\r\n" );
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document.write( "     You will get y = -5*(0-2.5)^2 + 75 = -5*2.5^2 + 75 = -5*6.25 + 75 = 43.75 meters.\r\n" );
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document.write( "(d)  To answer this question, equate the height to zero\r\n" );
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document.write( "         -5*(x-2.5)^2 + 75 = 0.\r\n" );
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document.write( "     Simplify step by step, solving this quadratic equation, and find x\r\n" );
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document.write( "         -5*(x-5)^2 = -75;\r\n" );
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document.write( "            (x-5)^2 = (-75)/(-5) = = 15;\r\n" );
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document.write( "            x - 5 = sqrt(15) = 3.873 seconds;\r\n" );
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document.write( "            x = 3.873 + 5 = 8.873 seconds.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved in full.\r<BR>\n" );
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