document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971832>Question 971832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.\r<BR>\n" );
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document.write( "Write an equation to model the height h in feet of the ball t seconds after it has been punted.<BR>\n" );
document.write( "The football is caught at 5.5 feet above the ground. How long was the football in the air?<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 #594229 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594229\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.\r<BR>\n" );
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document.write( "Write an equation to model the height h in feet of the ball t seconds after it has been punted.<BR>\n" );
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document.write( "32 ft/sec/sec is often used for gravity on Earth<BR>\n" );
document.write( "--> h(t) = -16t^2 + 45t + 2.5<BR>\n" );
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document.write( "The football is caught at 5.5 feet above the ground. How long was the football in the air?<BR>\n" );
document.write( "h(t) = -16t^2 + 45t + 2.5 = 5.5<BR>\n" );
document.write( "-16t^2 + 45t - 3 = 0<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B45x%2B-3+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B45x%2B-3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
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document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2845%29%5E2-4%2A-16%2A-3=1833 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2845%29%5E2-4%2A-16%2A-3=1833\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1833 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-45%2B-sqrt%28+1833+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-45%2B-sqrt%28+1833+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2845%29%2Bsqrt%28+1833+%29%29%2F2%5C-16+=+0.0683265857120221 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2845%29%2Bsqrt%28+1833+%29%29%2F2%5C-16+=+0.0683265857120221\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2845%29-sqrt%28+1833+%29%29%2F2%5C-16+=+2.74417341428798 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2845%29-sqrt%28+1833+%29%29%2F2%5C-16+=+2.74417341428798\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B45x%2B-3 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B45x%2B-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B45x%2B-3+=+%28x-0.0683265857120221%29%2A%28x-2.74417341428798%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B45x%2B-3+=+%28x-0.0683265857120221%29%2A%28x-2.74417341428798%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.0683265857120221, 2.74417341428798.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B45%2Ax%2B-3+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B45%2Ax%2B-3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t =~ 0.068 seconds ascending thru 5.5 ft<BR>\n" );
document.write( "t =~ 2.744 seconds when caught<BR>\n" );
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