document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277224>Question 277224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I would really just appreciate if someone can guide me an the formulas to use.  This is credit, and we havent done this chapter.  Much appreciated...\r<BR>\n" );
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document.write( "A miniature rocket is launched so that its height h in meters after t seconds is given by the equation h = -4.9t^2 + 19.6t + 10\r<BR>\n" );
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document.write( "a.  draw a graph of the equation<BR>\n" );
document.write( "b.  how high is it after 3 sec?<BR>\n" );
document.write( "c.  what is the max height the rocket will attain?<BR>\n" );
document.write( "d. How long after the launch will the rocket hit the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201963 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=201963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A miniature rocket is launched so that its height h in meters after t seconds is given by the equation h = -4.9t^2 + 19.6t + 10 <BR>\n" );
document.write( "a. draw a graph of the equation<BR>\n" );
document.write( "b. how high is it after 3 sec?<BR>\n" );
document.write( "Sub 3 for t<BR>\n" );
document.write( "h(3) = -4.9*9 + 19.6*3 + 10<BR>\n" );
document.write( "= 24.7 meters<BR>\n" );
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document.write( "c. what is the max height the rocket will attain?<BR>\n" );
document.write( "Max height is at the vertex, t = -b/2a<BR>\n" );
document.write( "t = -19.6/2*-4.9 = 2 seconds<BR>\n" );
document.write( "h(2) = -19.6 + 39.2 + 10<BR>\n" );
document.write( "h(2) = 29.6 meters max height<BR>\n" );
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document.write( "d. How long after the launch will the rocket hit the ground?<BR>\n" );
document.write( "It impacts at h = 0<BR>\n" );
document.write( "-4.9t^2 + 19.6t + 10<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=-4.9x%5E2%2B19.6x%2B10+=+0 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B19.6x%2B10+=+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=%2819.6%29%5E2-4%2A-4.9%2A10=580.16 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2819.6%29%5E2-4%2A-4.9%2A10=580.16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=580.16 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+=+%28-19.6%2B-sqrt%28+580.16+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-19.6%2B-sqrt%28+580.16+%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-%2819.6%29%2Bsqrt%28+580.16+%29%29%2F2%5C-4.9+=+-0.457807219155036 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2819.6%29%2Bsqrt%28+580.16+%29%29%2F2%5C-4.9+=+-0.457807219155036\"   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-%2819.6%29-sqrt%28+580.16+%29%29%2F2%5C-4.9+=+4.45780721915504 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2819.6%29-sqrt%28+580.16+%29%29%2F2%5C-4.9+=+4.45780721915504\"   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%2B19.6x%2B10 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B19.6x%2B10\"   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%2B19.6x%2B10+=+%28x--0.457807219155036%29%2A%28x-4.45780721915504%29 ALIGN=MIDDLE  ALT=\"-4.9x%5E2%2B19.6x%2B10+=+%28x--0.457807219155036%29%2A%28x-4.45780721915504%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.457807219155036, 4.45780721915504.\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%2B19.6%2Ax%2B10+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B19.6%2Ax%2B10+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "t = x<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );