document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=604841>Question 604841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help my in How to solve quadratic function word problems<BR>\n" );
document.write( "my question is<BR>\n" );
document.write( "A ball is released 6 feet above the ground and thrown vertically into the air. The equation h=-16t^+112t+6 gives the height of the ball if the initial is 112 feet per second.<BR>\n" );
document.write( "1. Write the equation of the axis of symmetry and find the coordinates of the vertex of the graph of the equation.<BR>\n" );
document.write( "2. What is the maximum height above the ground that the ball reaches?<BR>\n" );
document.write( "3. How many seconds is the ball in the air? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381456 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=381456\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is released 6 feet above the ground and thrown vertically into the air. The equation h=-16t^+112t+6 gives the height of the ball if the initial is 112 feet per second.<BR>\n" );
document.write( "1. Write the equation of the axis of symmetry and find the coordinates of the vertex of the graph of the equation.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "axis of symmetry:<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -112/(2(-16))<BR>\n" );
document.write( "x = -112/(-32)<BR>\n" );
document.write( "x = 3.5 (vertical line crossing at x=3.5)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "find, y-value when x=3.5:<BR>\n" );
document.write( "-16t^+112t+6<BR>\n" );
document.write( "-16(3.5)^+112(3.5)+6<BR>\n" );
document.write( "202<BR>\n" );
document.write( "So, vertex is at (3.5, 202)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2. What is the maximum height above the ground that the ball reaches?<BR>\n" );
document.write( "202 feet<BR>\n" );
document.write( "3. How many seconds is the ball in the air?<BR>\n" );
document.write( "set h=0 and solve for t:<BR>\n" );
document.write( "h=-16t^+112t+6<BR>\n" );
document.write( "0=-16t^+112t+6<BR>\n" );
document.write( "applying the \"quadratic formula\" gives us:<BR>\n" );
document.write( "x  {-0.1, 7.1}<BR>\n" );
document.write( "we can throw out the negative solution (extraneous) leaving<BR>\n" );
document.write( "x = 7.1 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic formula follows:<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=-16x%5E2%2B112x%2B6+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B112x%2B6+=+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=%28112%29%5E2-4%2A-16%2A6=12928 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28112%29%5E2-4%2A-16%2A6=12928\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=12928 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+=+%28-112%2B-sqrt%28+12928+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-112%2B-sqrt%28+12928+%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-%28112%29%2Bsqrt%28+12928+%29%29%2F2%5C-16+=+-0.0531676008879738 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28112%29%2Bsqrt%28+12928+%29%29%2F2%5C-16+=+-0.0531676008879738\"   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-%28112%29-sqrt%28+12928+%29%29%2F2%5C-16+=+7.05316760088797 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28112%29-sqrt%28+12928+%29%29%2F2%5C-16+=+7.05316760088797\"   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%2B112x%2B6 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B112x%2B6\"   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%2B112x%2B6+=+-16%28x--0.0531676008879738%29%2A%28x-7.05316760088797%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B112x%2B6+=+-16%28x--0.0531676008879738%29%2A%28x-7.05316760088797%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.0531676008879738, 7.05316760088797.\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%2B112%2Ax%2B6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B112%2Ax%2B6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );