document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183267>Question 1183267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi can you please help me with this question. A golf ball is hit from the top of a tee. The quadratic equation y=-5x^2 + 20x + 0.05 describes its height,y, in metres as time,x, in seconds passes. Determine how long the ball is in the air. Thanks for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813493 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=813493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "A golf ball is hit from the top of a tee. The quadratic equation <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5x%5E2+%2B+20x+%2B+0.05+ ALIGN=MIDDLE  ALT=\"y=-5x%5E2+%2B+20x+%2B+0.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "describes its height, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in metres as time,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in seconds passes. \r<BR>\n" );
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document.write( "Determine how long the ball is in the air. \r<BR>\n" );
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document.write( "First, you have to determine how long it will take for the golf ball to reach its maximum height.\r<BR>\n" );
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document.write( "so, rewrite equation in vertex form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > are coordinates of vertex\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5x%5E2+%2B+20x+%2B+0.05+ ALIGN=MIDDLE  ALT=\"y=-5x%5E2+%2B+20x+%2B+0.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....group<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5x%5E2+%2B+20x%29+%2B+0.05+ ALIGN=MIDDLE  ALT=\"y=%28-5x%5E2+%2B+20x%29+%2B+0.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%28x%5E2+-4x%29+%2B+0.05+ ALIGN=MIDDLE  ALT=\"y=-5%28x%5E2+-4x%29+%2B+0.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%28x%5E2+-4x%2Bb%5E2%29+-%28-5b%5E2%29%2B+0.05+ ALIGN=MIDDLE  ALT=\"y=-5%28x%5E2+-4x%2Bb%5E2%29+-%28-5b%5E2%29%2B+0.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4%2F2=2 ALIGN=MIDDLE  ALT=\"b=4%2F2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%28x%5E2+-4x%2B2%5E2%29+%2B5%2A2%5E2%2B+0.05+ ALIGN=MIDDLE  ALT=\"y=-5%28x%5E2+-4x%2B2%5E2%29+%2B5%2A2%5E2%2B+0.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%28x+-2%29%5E2+%2B20%2B+0.05+ ALIGN=MIDDLE  ALT=\"y=-5%28x+-2%29%5E2+%2B20%2B+0.05+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-5%28x+-2%29%5E2+%2B20.05+ ALIGN=MIDDLE  ALT=\"y=-5%28x+-2%29%5E2+%2B20.05+\"   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=2 ALIGN=MIDDLE  ALT=\"h=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=20.05 ALIGN=MIDDLE  ALT=\"k=20.05\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to reach its maximum height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20.05 ALIGN=MIDDLE  ALT=\"20.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it will take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds\r<BR>\n" );
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document.write( "The time in the air is twice the one I found solving for t where the height is maximum.\r<BR>\n" );
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document.write( "the ball is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds in the air\r<BR>\n" );
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document.write( " </SPAN>\n" );
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