document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013573>Question 1013573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height h (in feet) above the ground of a baseball depends upon the time t (in seconds) it has been in flight. Cameron takes a mighty swing, but hits a bloop sinlge whose height is described approximately by the equation h=-5t^2+45t+17. Ho long is the ball in the air? The ball reaches its maximum heght after how many seconds of light? What is the maximum height?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629995 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=629995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height h (in feet) above the ground of a baseball depends upon the time t (in seconds) it has been in flight. Cameron takes a mighty swing, but hits a bloop sinlge whose height is described approximately by the equation h=-5t^2+45t+17.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Ho long is the ball in the air? <BR>\n" );
document.write( "The ball reaches its maximum height after how many seconds of light?<BR>\n" );
document.write( "Max ht is the vertex of the parabola.<BR>\n" );
document.write( "@t = -b/2a = -45/-10 = 4.5 seconds<BR>\n" );
document.write( "----<BR>\n" );
document.write( "How long is the ball in the air?<BR>\n" );
document.write( "h=-5t^2+45t+17<BR>\n" );
document.write( "Find t when h = 0<BR>\n" );
document.write( "-5t^2+45t+17 = 0<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=-5x%5E2%2B45x%2B17+=+0 ALIGN=MIDDLE  ALT=\"-5x%5E2%2B45x%2B17+=+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=%2845%29%5E2-4%2A-5%2A17=2365 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2845%29%5E2-4%2A-5%2A17=2365\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2365 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+=+%28-45%2B-sqrt%28+2365+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-45%2B-sqrt%28+2365+%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-%2845%29%2Bsqrt%28+2365+%29%29%2F2%5C-5+=+-0.363126566315131 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2845%29%2Bsqrt%28+2365+%29%29%2F2%5C-5+=+-0.363126566315131\"   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-%2845%29-sqrt%28+2365+%29%29%2F2%5C-5+=+9.36312656631513 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2845%29-sqrt%28+2365+%29%29%2F2%5C-5+=+9.36312656631513\"   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=-5x%5E2%2B45x%2B17 ALIGN=MIDDLE  ALT=\"-5x%5E2%2B45x%2B17\"   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=-5x%5E2%2B45x%2B17+=+%28x--0.363126566315131%29%2A%28x-9.36312656631513%29 ALIGN=MIDDLE  ALT=\"-5x%5E2%2B45x%2B17+=+%28x--0.363126566315131%29%2A%28x-9.36312656631513%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.363126566315131, 9.36312656631513.\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+-5%2Ax%5E2%2B45%2Ax%2B17+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B45%2Ax%2B17+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the negative.<BR>\n" );
document.write( "t =~ 9.363 seconds<BR>\n" );
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document.write( "What is the maximum height?<BR>\n" );
document.write( "= -5*4.5^2 + 45*4.5 + 17<BR>\n" );
document.write( "= 118.25 feet\r<BR>\n" );
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document.write( "Usually -5t^2 or -4.9t^2 is use for heights in meters.<BR>\n" );
document.write( "-16t^2 is used for feet. </SPAN>\n" );
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