document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=457645>Question 457645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An object launched upward with initial velocity of 4.9 m/s from a height of 9.8 m will have a height of, S(t)=-4.9t^2+4.9t+9.8, where S is in meters and t is in seconds.<BR>\n" );
document.write( "a). How long will it take the object to hit the ground?<BR>\n" );
document.write( "b). Find the interval on which the height of the object is greater than 2.8 m. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315679 by </B><A HREF=/tutors/aboutme.mpl?userid=jorel1380><B>jorel1380(3719)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jorel1380><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=jorel1380><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> s=-4.9t2+4.9t+9.8<BR>\n" );
document.write( "4.9t2-4.9t-9.8=0<BR>\n" );
document.write( "t2-t-2=0<BR>\n" );
document.write( "(t+1)(t-2)=0<BR>\n" );
document.write( "t=2 or -1<BR>\n" );
document.write( "Throwing out the negative answer, the object will hit the ground in 2 seconds.<BR>\n" );
document.write( "2.8<-4.9t2+4.9t+9.8<BR>\n" );
document.write( "0<-4.9t2+4.9t+7<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=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=-4.9x%5E2%2B4.9x%2B7+=+0 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B4.9x%2B7+=+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=%284.9%29%5E2-4%2A-4.9%2A7=161.21 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284.9%29%5E2-4%2A-4.9%2A7=161.21\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=161.21 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+=+%28-4.9%2B-sqrt%28+161.21+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4.9%2B-sqrt%28+161.21+%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-%284.9%29%2Bsqrt%28+161.21+%29%29%2F2%5C-4.9+=+-0.795596939086932 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%284.9%29%2Bsqrt%28+161.21+%29%29%2F2%5C-4.9+=+-0.795596939086932\"   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-%284.9%29-sqrt%28+161.21+%29%29%2F2%5C-4.9+=+1.79559693908693 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%284.9%29-sqrt%28+161.21+%29%29%2F2%5C-4.9+=+1.79559693908693\"   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=-4.9x%5E2%2B4.9x%2B7 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B4.9x%2B7\"   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=-4.9x%5E2%2B4.9x%2B7+=+-4.9%28x--0.795596939086932%29%2A%28x-1.79559693908693%29 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B4.9x%2B7+=+-4.9%28x--0.795596939086932%29%2A%28x-1.79559693908693%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.795596939086932, 1.79559693908693.\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+-4.9%2Ax%5E2%2B4.9%2Ax%2B7+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B4.9%2Ax%2B7+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "The area in the upper right quadrant in your graph represents the time the object is above 2.8 meters.. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );