document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246760>Question 246760</A>: <I><SPAN STYLE=\"word-break: break-all;\">    Foul Ball\r<BR>\n" );
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document.write( "Suppose Charlie O'Brian of the Braves hits a baseball straight upward at 150 ft/sec from a height of 5ft.\r<BR>\n" );
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document.write( "Use the formula to determine how long does it takes the ball to return to the earth.\r<BR>\n" );
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document.write( "Estimate the maximum height reached by the ball\r<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 #180107 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=180107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose Charlie O'Brian of the Braves hits a baseball straight upward at 150 ft/sec from a height of 5ft. \r<BR>\n" );
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document.write( "Use the formula to determine how long does it takes the ball to return to the earth.<BR>\n" );
document.write( "h(t) =-16t^2 + 150t + 5 (h in feet, t in seconds)<BR>\n" );
document.write( "To find the time of impact, set h(t) = 0<BR>\n" );
document.write( "-16t^2 + 150t + 5 = 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%2B150x%2B5+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B150x%2B5+=+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" );
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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=%28150%29%5E2-4%2A-16%2A5=22820 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28150%29%5E2-4%2A-16%2A5=22820\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=22820 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+=+%28-150%2B-sqrt%28+22820+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-150%2B-sqrt%28+22820+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28150%29%2Bsqrt%28+22820+%29%29%2F2%5C-16+=+-0.0332156501954231 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28150%29%2Bsqrt%28+22820+%29%29%2F2%5C-16+=+-0.0332156501954231\"   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-%28150%29-sqrt%28+22820+%29%29%2F2%5C-16+=+9.40821565019542 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28150%29-sqrt%28+22820+%29%29%2F2%5C-16+=+9.40821565019542\"   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%2B150x%2B5 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B150x%2B5\"   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%2B150x%2B5+=+%28x--0.0332156501954231%29%2A%28x-9.40821565019542%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B150x%2B5+=+%28x--0.0332156501954231%29%2A%28x-9.40821565019542%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.0332156501954231, 9.40821565019542.\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%2B150%2Ax%2B5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B150%2Ax%2B5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Sub t for x, the solver uses x<BR>\n" );
document.write( "Ignore the negative time.<BR>\n" );
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document.write( "Estimate the maximum height reached by the ball <BR>\n" );
document.write( "That's at the vertex of the parabola.<BR>\n" );
document.write( "t = -b/2a = -150/-32<BR>\n" );
document.write( "t = 75/16 seconds<BR>\n" );
document.write( "h(75/16) = -16*(75/16)^2 + 150*75/16 + 5<BR>\n" );
document.write( "h = - 5625/16 + 11250/16 + 80/16<BR>\n" );
document.write( "h = 5705/16 feet<BR>\n" );
document.write( "h = 356.5625 feet exactly<BR>\n" );
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