document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=747342>Question 747342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> h = –16t^2 + vt + c\r<BR>\n" );
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document.write( "The equation shown above is the vertical motion formula, where h is the ending height, t is the time in seconds, v is the starting velocity in feet per second, and c is the starting height in feet.\r<BR>\n" );
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document.write( "If Adam, who is 6 feet tall, threw his baseball 80 feet per second straight up into the air, which of the following answers is the best estimate of how long it took the ball to come back to the ground?\r<BR>\n" );
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document.write( "I think this is the equation, h= -16t^2+80t+6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454846 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h= -16t^2+80t+6 (is correct)<BR>\n" );
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document.write( "when the ball is on the ground, h is zero.  So, set h to zero and solve for t:<BR>\n" );
document.write( "0 = -16t^2+80t+6<BR>\n" );
document.write( "0 = 16t^2-80t-6<BR>\n" );
document.write( "0 = 8t^2-40t-3<BR>\n" );
document.write( "solve using the \"quadratic formula\" yields:<BR>\n" );
document.write( "x = {5.07, -0.07}<BR>\n" );
document.write( "throw out the negative value (extraneous) leaving<BR>\n" );
document.write( "x = 5.07 seconds<BR>\n" );
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document.write( "Details of quadratic formula follows:<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=quadratic.solver>SOLVE quadratic equation with variable</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=8x%5E2%2B-40x%2B-3+=+0 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-40x%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" );
document.write( "  <BR>\n" );
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=%28-40%29%5E2-4%2A8%2A-3=1696 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-40%29%5E2-4%2A8%2A-3=1696\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1696 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--40%2B-sqrt%28+1696+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--40%2B-sqrt%28+1696+%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-%28-40%29%2Bsqrt%28+1696+%29%29%2F2%5C8+=+5.07390753524675 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1696+%29%29%2F2%5C8+=+5.07390753524675\"   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-%28-40%29-sqrt%28+1696+%29%29%2F2%5C8+=+-0.0739075352467502 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-40%29-sqrt%28+1696+%29%29%2F2%5C8+=+-0.0739075352467502\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2%2B-40x%2B-3 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-40x%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=8x%5E2%2B-40x%2B-3+=+8%28x-5.07390753524675%29%2A%28x--0.0739075352467502%29 ALIGN=MIDDLE  ALT=\"8x%5E2%2B-40x%2B-3+=+8%28x-5.07390753524675%29%2A%28x--0.0739075352467502%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5.07390753524675, -0.0739075352467502.\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+8%2Ax%5E2%2B-40%2Ax%2B-3+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-40%2Ax%2B-3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );