document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930432>Question 930432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this: A penny is thrown up in the air from a building. Its height in feet after x seconds is given by: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16x%5E2+%2B24x%2B75+ ALIGN=MIDDLE  ALT=\"+-16x%5E2+%2B24x%2B75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a) when does it reach it's max height?<BR>\n" );
document.write( "b) what is its max height?<BR>\n" );
document.write( "c) when does it hit the ground?\r<BR>\n" );
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document.write( "For (c) I started to solve it with the quadratic formula but wasn't getting a sensible answer. I'm not sure how to set up the other two. <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 #565006 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=565006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A penny is thrown up in the air from a building. Its height in feet after x seconds is given by: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16x%5E2+%2B24x%2B75+ ALIGN=MIDDLE  ALT=\"+-16x%5E2+%2B24x%2B75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a) when does it reach it's [sic] max height?<BR>\n" );
document.write( "It's the vertex of the parabola, at x = -b/2a<BR>\n" );
document.write( "x = -24/-32 seconds = 3/4 seconds<BR>\n" );
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document.write( "b) what is its max height?<BR>\n" );
document.write( "h(x) = -16*(3/4)^2 + 24*(3/4) + 75<BR>\n" );
document.write( "= -9 + 18 + 75<BR>\n" );
document.write( "= 84 ft<BR>\n" );
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document.write( "c) when does it hit the ground?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16x%5E2+%2B24x%2B75+=+0 ALIGN=MIDDLE  ALT=\"+-16x%5E2+%2B24x%2B75+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=-16x%5E2%2B24x%2B75+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B24x%2B75+=+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=%2824%29%5E2-4%2A-16%2A75=5376 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2824%29%5E2-4%2A-16%2A75=5376\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5376 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+=+%28-24%2B-sqrt%28+5376+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-24%2B-sqrt%28+5376+%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-%2824%29%2Bsqrt%28+5376+%29%29%2F2%5C-16+=+-1.54128784747792 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+5376+%29%29%2F2%5C-16+=+-1.54128784747792\"   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-%2824%29-sqrt%28+5376+%29%29%2F2%5C-16+=+3.04128784747792 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2824%29-sqrt%28+5376+%29%29%2F2%5C-16+=+3.04128784747792\"   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%2B24x%2B75 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B24x%2B75\"   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%2B24x%2B75+=+%28x--1.54128784747792%29%2A%28x-3.04128784747792%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B24x%2B75+=+%28x--1.54128784747792%29%2A%28x-3.04128784747792%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.54128784747792, 3.04128784747792.\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%2B24%2Ax%2B75+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B24%2Ax%2B75+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "Ignore the negative solution.<BR>\n" );
document.write( "x =~ 3.041 seconds\r<BR>\n" );
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document.write( "For (c) I started to solve it with the quadratic formula but wasn't getting a sensible answer. I'm not sure how to set up the other two. <BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );