document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188443>Question 1188443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A stone is tossed from a bridge into the river below. Its path is represented by h = -2t^2 + 7t + 9, where h is height, in metres, and t is time, in seconds.<BR>\n" );
document.write( "Find the maximum height reached by the stone.<BR>\n" );
document.write( "How many seconds does it take to reach the maximum height?<BR>\n" );
document.write( "How many seconds does it take for the stone to reach the water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819516 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=819516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-2t%5E2+%2B+7t+%2B+9 ALIGN=MIDDLE  ALT=\"h+=+-2t%5E2+%2B+7t+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is height, in metres, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+ ALIGN=MIDDLE  ALT=\"t+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is time, in seconds.\r<BR>\n" );
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document.write( "Find the maximum height reached by the stone.<BR>\n" );
document.write( "since you have a parabola that opens downward, maximum will be at vertex<BR>\n" );
document.write( "so, rewrite equation in vertx form by completing square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%28-2t%5E2+%2B+7t%29+%2B+9 ALIGN=MIDDLE  ALT=\"h=%28-2t%5E2+%2B+7t%29+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >......factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-2%28t%5E2+-+%287%2F2%29t%29+%2B+9 ALIGN=MIDDLE  ALT=\"h=-2%28t%5E2+-+%287%2F2%29t%29+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-2%28t%5E2+-+%287%2F2%29t%2Bb%5E2%29+-%28-2b%5E2%29%2B+9 ALIGN=MIDDLE  ALT=\"h=-2%28t%5E2+-+%287%2F2%29t%2Bb%5E2%29+-%28-2b%5E2%29%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%287%2F2%29%2F2=7%2F4%29 ALIGN=MIDDLE  ALT=\"b=%287%2F2%29%2F2=7%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-2%28t%5E2+-+%287%2F2%29t%2B%287%2F4%29%5E2%29+%2B2%287%2F4%29%5E2%2B+9 ALIGN=MIDDLE  ALT=\"h=-2%28t%5E2+-+%287%2F2%29t%2B%287%2F4%29%5E2%29+%2B2%287%2F4%29%5E2%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-2%28t+-+7%2F4%29%5E2+%2B2%2849%2F16%29%2B+9 ALIGN=MIDDLE  ALT=\"h=-2%28t+-+7%2F4%29%5E2+%2B2%2849%2F16%29%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-2%28t+-+7%2F4%29%5E2+%2B121%2F8 ALIGN=MIDDLE  ALT=\"h=-2%28t+-+7%2F4%29%5E2+%2B121%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> vertex is at (7/4,121/8)\r<BR>\n" );
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document.write( "so, the maximum height reached by the stone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=121%2F8 ALIGN=MIDDLE  ALT=\"h=121%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=15.125 ALIGN=MIDDLE  ALT=\"h=15.125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How many seconds does it take to reach the maximum height?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-2t%5E2+%2B+7t+%2B+9 ALIGN=MIDDLE  ALT=\"h+=+-2t%5E2+%2B+7t+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >....plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=15.125 ALIGN=MIDDLE  ALT=\"h=15.125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.125+=+-2t%5E2+%2B+7t+%2B+9 ALIGN=MIDDLE  ALT=\"15.125+=+-2t%5E2+%2B+7t+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%5E2+-+7t+%2B+6.125+=+0 ALIGN=MIDDLE  ALT=\"2t%5E2+-+7t+%2B+6.125+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....using quadratic formula we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.75 ALIGN=MIDDLE  ALT=\"t=1.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds\r<BR>\n" );
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document.write( "How many seconds does it take for the stone to reach the water?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-2t%5E2+%2B+7t+%2B+9 ALIGN=MIDDLE  ALT=\"0+=+-2t%5E2+%2B+7t+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >....plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-2t%5E2+%2B+7t+%2B+9 ALIGN=MIDDLE  ALT=\"0+=+-2t%5E2+%2B+7t+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >......factor<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-%28t+%2B+1%29+%282t+-+9%29 ALIGN=MIDDLE  ALT=\"0+=+-%28t+%2B+1%29+%282t+-+9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-1 ALIGN=MIDDLE  ALT=\"t+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> disregard negative time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+9%2F2 ALIGN=MIDDLE  ALT=\"t+=+9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+4.5 ALIGN=MIDDLE  ALT=\"t+=+4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "it takes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5 ALIGN=MIDDLE  ALT=\"4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds  for the stone to reach the water\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );