document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058616>Question 1058616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> height y (in feet) of punted football is approximated by y = -16/2025 x^2 +9/5x + 5/2   where x is horizontal distance (in feet ) from point at which the ball is punted .<BR>\n" );
document.write( "(a)use a graphing utility to graph the path of football.<BR>\n" );
document.write( "(b)how high is the ball when it is punted ?(find y when x=0)<BR>\n" );
document.write( "(c)what is the maximum height of football?(round your answer to two decimal places)<BR>\n" );
document.write( "(d)how far from punter does the football strike the ground?(round your answer to two decimal places)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673724 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=673724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> height y (in feet) of punted football is approximated by y = -16/2025 x^2 +9/5x + 5/2   where x is horizontal distance (in feet ) from point at which the ball is punted.<BR>\n" );
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document.write( "(a)use a graphing utility to graph the path of football.<BR>\n" );
document.write( "dl the FREE graph software at www.padowan.dk<BR>\n" );
document.write( "Use Insert, enter -16x^2/2025 + 9x/5 + 5/2<BR>\n" );
document.write( "Pick a color<BR>\n" );
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document.write( "(b)how high is the ball when it is punted ?(find y when x=0)<BR>\n" );
document.write( "2.5 feet<BR>\n" );
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document.write( "(c)what is the maximum height of football?(round your answer to two decimal places)<BR>\n" );
document.write( "It's the vertex of the parabola at x = -b/2a<BR>\n" );
document.write( "x = (-9/5)/(-32/2025) = 9*2025/150 = 121.5<BR>\n" );
document.write( "y = 31.66 feet<BR>\n" );
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document.write( "(d)how far from punter does the football strike the ground?(round your answer to two decimal places)<BR>\n" );
document.write( "Find x when y = 0<BR>\n" );
document.write( "y = -16/2025 x^2 +9/5x + 5/2 = 0<BR>\n" );
document.write( "16x^2 - 3645x - 5062.5 = 0<BR>\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%2B-3645x%2B-5062.5+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-3645x%2B-5062.5+=+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=%28-3645%29%5E2-4%2A16%2A-5062.5=13610025 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-3645%29%5E2-4%2A16%2A-5062.5=13610025\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=13610025 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--3645%2B-sqrt%28+13610025+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--3645%2B-sqrt%28+13610025+%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-%28-3645%29%2Bsqrt%28+13610025+%29%29%2F2%5C16+=+229.19302304471 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-3645%29%2Bsqrt%28+13610025+%29%29%2F2%5C16+=+229.19302304471\"   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-%28-3645%29-sqrt%28+13610025+%29%29%2F2%5C16+=+-1.38052304471012 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-3645%29-sqrt%28+13610025+%29%29%2F2%5C16+=+-1.38052304471012\"   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%2B-3645x%2B-5062.5 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-3645x%2B-5062.5\"   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%2B-3645x%2B-5062.5+=+%28x-229.19302304471%29%2A%28x--1.38052304471012%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-3645x%2B-5062.5+=+%28x-229.19302304471%29%2A%28x--1.38052304471012%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 229.19302304471, -1.38052304471012.\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%2B-3645%2Ax%2B-5062.5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-3645%2Ax%2B-5062.5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "======<BR>\n" );
document.write( "Ignore the negative value<BR>\n" );
document.write( "x =~ 229.19 feet<BR>\n" );
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