document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=749959>Question 749959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the absence of air resistance, the trajectory of a cannon ball fired from ground level at 1200 feet per second and at an angle of 45o can be approximated as\r<BR>\n" );
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document.write( "y=x-1/45,000x^2\r<BR>\n" );
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document.write( "where y is the height above the ground and x is the distance from the cannon.\r<BR>\n" );
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document.write( "A. Find the vertex of the parabola described by this equation\r<BR>\n" );
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document.write( "B. What is the maximum height of the cannon ball?\r<BR>\n" );
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document.write( "C. What is the range of the cannon ball (the range is the horizontal distance to the point of impact at ground level)?\r<BR>\n" );
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document.write( "I'm a bit confused on how to find all these! Any help is appreciated thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456273 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the absence of air resistance, the trajectory of a cannon ball fired from ground level at 1200 feet per second and at an angle of 45 degrees can be approximated as<BR>\n" );
document.write( "y=x-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F45000 ALIGN=MIDDLE  ALT=\"1%2F45000\"   DISABLED_style= \"max-width:90%; height:auto;\" >x^2<BR>\n" );
document.write( "WRite this in the standard form: y = ax^2 + bx + c<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F45000 ALIGN=MIDDLE  ALT=\"-1%2F45000\"   DISABLED_style= \"max-width:90%; height:auto;\" >x^2 + x<BR>\n" );
document.write( "where y is the height above the ground and x is the distance from the cannon.<BR>\n" );
document.write( "A. Find the vertex of the parabola described by this equation<BR>\n" );
document.write( "Find the axis of symmetry which is x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%282%2A%28-1%2F45000%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%282%2A%28-1%2F45000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2F%28%28-2%2F45000%29%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2F%28%28-2%2F45000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +22500<BR>\n" );
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document.write( "B. What is the maximum height of the cannon ball?<BR>\n" );
document.write( "Replace x with 22500 in the original equation, find y<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F45000 ALIGN=MIDDLE  ALT=\"-1%2F45000\"   DISABLED_style= \"max-width:90%; height:auto;\" >22500^2 + 22500<BR>\n" );
document.write( "y = +11250 ft max height<BR>\n" );
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document.write( "C. What is the range of the cannon ball (the range is the horizontal distance to the point of impact at ground level)?<BR>\n" );
document.write( "At impact, y = 0, occurs twice the value of the axis of symmetry<BR>\n" );
document.write( "x = 2(22500) = 45000 ft<BR>\n" );
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document.write( "Graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10000%2C+50000%2C+-2000%2C+15000%2C+%28-1%2F45000%29x%5E2%2Bx%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10000%2C+50000%2C+-2000%2C+15000%2C+%28-1%2F45000%29x%5E2%2Bx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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