document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980221>Question 980221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need help with the detail of solving this problem.  Can someone please show me the step by step process in figuring out this problem?  \r<BR>\n" );
document.write( "\n" );
document.write( "I have tried to calculate it many times and cannot for the life of me come up with the correct answer.\r<BR>\n" );
document.write( "\n" );
document.write( "I am familiar with the quadratic formula but for some reason cannot get it to work for this problem.\r<BR>\n" );
document.write( "\n" );
document.write( "“An object is thrown directly upward from a starting height of 25 ft and a starting velocity of 85 ft per second. The following function describes the height of the object with respect to the time, t.”\r<BR>\n" );
document.write( "\n" );
document.write( "h(t) = -16t2 + 85t + 25\r<BR>\n" );
document.write( "\n" );
document.write( "How long does it take before the object reaches the ground? Round you answer to \r<BR>\n" );
document.write( "\n" );
document.write( "the nearest hundredths place.\r<BR>\n" );
document.write( "\n" );
document.write( "The answer is 5.59.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601413 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=601413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> “An object is thrown directly upward from a starting height of 25 ft and a starting velocity of 85 ft per second. The following function describes the height of the object with respect to the time, t.”\r<BR>\n" );
document.write( "\n" );
document.write( "h(t) = -16t2 + 85t + 25\r<BR>\n" );
document.write( "\n" );
document.write( "How long does it take before the object reaches the ground? Round you answer to \r<BR>\n" );
document.write( "\n" );
document.write( "the nearest hundredths place.\r<BR>\n" );
document.write( "\n" );
document.write( "The answer is 5.59.<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Use ^ (Shift 6) for exponents.\r<BR>\n" );
document.write( "\n" );
document.write( "h(t) = -16t^2 + 85t + 25<BR>\n" );
document.write( "It hits the ground when h(t) = 0<BR>\n" );
document.write( "---\r<BR>\n" );
document.write( "\n" );
document.write( "h(t) = -16t^2 + 85t + 25 = 0<BR>\n" );
document.write( "Solve for t<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%2B85x%2B25+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B85x%2B25+=+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=%2885%29%5E2-4%2A-16%2A25=8825 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2885%29%5E2-4%2A-16%2A25=8825\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=8825 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+=+%28-85%2B-sqrt%28+8825+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-85%2B-sqrt%28+8825+%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-%2885%29%2Bsqrt%28+8825+%29%29%2F2%5C-16+=+-0.27942097313374 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2885%29%2Bsqrt%28+8825+%29%29%2F2%5C-16+=+-0.27942097313374\"   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-%2885%29-sqrt%28+8825+%29%29%2F2%5C-16+=+5.59192097313374 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2885%29-sqrt%28+8825+%29%29%2F2%5C-16+=+5.59192097313374\"   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=-16x%5E2%2B85x%2B25 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B85x%2B25\"   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%2B85x%2B25+=+%28x--0.27942097313374%29%2A%28x-5.59192097313374%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B85x%2B25+=+%28x--0.27942097313374%29%2A%28x-5.59192097313374%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.27942097313374, 5.59192097313374.\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%2B85%2Ax%2B25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B85%2Ax%2B25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "=================<BR>\n" );
document.write( "t = ~ 5.59 seconds<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Ignore the negative solution.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );