document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1153181>Question 1153181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by <BR>\n" );
document.write( "h(t) = −4.9t2 + 18t + 8.<BR>\n" );
document.write( " How long does it take to reach maximum height? (Round your answer to three decimal places.)<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 #775352 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=775352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+%2B+18t+%2B+8 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+%2B+18t+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+ ALIGN=MIDDLE  ALT=\"h%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=height ALIGN=MIDDLE  ALT=\"height\"   DISABLED_style= \"max-width:90%; height:auto;\" > in meters above the ground<BR>\n" );
document.write( "<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 the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=time ALIGN=MIDDLE  ALT=\"time\"   DISABLED_style= \"max-width:90%; height:auto;\" > in seconds\r<BR>\n" );
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document.write( "This is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical ALIGN=MIDDLE  ALT=\"vertical\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+parabola ALIGN=MIDDLE  ALT=\"+parabola\"   DISABLED_style= \"max-width:90%; height:auto;\" > open <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=downward ALIGN=MIDDLE  ALT=\"downward\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=maximum ALIGN=MIDDLE  ALT=\"maximum\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The number of seconds it takes for the ball to reach the maximum height is equal to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-coordinate of the vertex.\r<BR>\n" );
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document.write( "Convert the given function to vertex form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+%2B+18t+%2B+8 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+%2B+18t+%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+%28-4.9t%5E2+-+18t+%29%2B+8 ALIGN=MIDDLE  ALT=\"h%28t%29+=+%28-4.9t%5E2+-+18t+%29%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >......factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9 ALIGN=MIDDLE  ALT=\"-4.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9%28t%5E2+-+%2818%2F4.9%29t+%29%2B+8 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9%28t%5E2+-+%2818%2F4.9%29t+%29%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......complete the squares\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9%28t%5E2+-+%2818%2F4.9%29t%2Bb%5E2+%29-%28-4.9%29b%5E2%2B+8 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9%28t%5E2+-+%2818%2F4.9%29t%2Bb%5E2+%29-%28-4.9%29b%5E2%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >......<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=+%2818%2F4.9%29 ALIGN=MIDDLE  ALT=\"2ab=+%2818%2F4.9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=+%2818%2F4.9%29 ALIGN=MIDDLE  ALT=\"2b=+%2818%2F4.9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=+%2818%2F4.9%29%2F2 ALIGN=MIDDLE  ALT=\"b=+%2818%2F4.9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=+%2818%2F9.8%29 ALIGN=MIDDLE  ALT=\"b=+%2818%2F9.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=180%2F98=90%2F49 ALIGN=MIDDLE  ALT=\"b=180%2F98=90%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9%28t%5E2+-+%2818%2F4.9%29t%2B%2890%2F49%29%5E2+%29%2B4.9%2890%2F49%29%5E2%2B+8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.9%2890%2F49%29%5E2=810%2F49+=+16.531 ALIGN=MIDDLE  ALT=\"4.9%2890%2F49%29%5E2=810%2F49+=+16.531\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9%28t+-+90%2F49%29%5E2+%2B16.531%2B+8 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9%28t+-+90%2F49%29%5E2+%2B16.531%2B+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2F49=1837 ALIGN=MIDDLE  ALT=\"90%2F49=1837\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9%28t+-+1.837%29%5E2+%2B24.531 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9%28t+-+1.837%29%5E2+%2B24.531\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=>the vertex is the point \r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.8 ALIGN=MIDDLE  ALT=\"1.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.531 ALIGN=MIDDLE  ALT=\"24.531\"   DISABLED_style= \"max-width:90%; height:auto;\" >)-> <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  coordinate\r<BR>\n" );
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document.write( "The number of seconds it takes for the ball to reach the maximum height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.837 ALIGN=MIDDLE  ALT=\"1.837\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );