document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374241>Question 374241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cannon fires a cannonball as shown in the figure. The path of the cannonball is a parabola with vertex at the highest point of the path. If the cannonball lands d = 600 ft from the cannon and the highest point it reaches is h = 1200 ft above the ground, find an equation for the path of the cannonball. Place the origin at the location of the cannon. <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 #266382 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=266382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cannon fires a cannonball as shown in the figure.<BR>\n" );
document.write( "The path of the cannonball is a parabola with vertex at the highest point of the path.<BR>\n" );
document.write( " If the cannonball lands d = 600 ft from the cannon and the highest point it<BR>\n" );
document.write( " reaches is h = 1200 ft above the ground, find an equation for the path of the cannonball. <BR>\n" );
document.write( "Place the origin at the location of the cannon.<BR>\n" );
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document.write( "Since the cannon ball starts at x=0 and lands x=600, the axis of symmetry = 300<BR>\n" );
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document.write( "Using the form ax^2 + bx + c = y, (c=0 in this problem)<BR>\n" );
document.write( "x=300; y=1200<BR>\n" );
document.write( "(300^2)a +  300b = 1200<BR>\n" );
document.write( "90000a + 300b = 1200<BR>\n" );
document.write( "Simplify, divide by 300, results<BR>\n" );
document.write( "300a + b = 4<BR>\n" );
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document.write( "x=600; y= 0<BR>\n" );
document.write( "36000a + 600b = 0<BR>\n" );
document.write( "Simplify, divide by 600<BR>\n" );
document.write( "600a + b = 0<BR>\n" );
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document.write( "Use elimination here<BR>\n" );
document.write( "600a + b = 0<BR>\n" );
document.write( "300a + b = 4<BR>\n" );
document.write( "---------------subtraction eliminates b, find a<BR>\n" );
document.write( "300a = -4<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2F300 ALIGN=MIDDLE  ALT=\"%28-4%29%2F300\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F75 ALIGN=MIDDLE  ALT=\"-1%2F75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find b using 300a + b = 4<BR>\n" );
document.write( "300(-1/75) = b <BR>\n" );
document.write( "-4 + b = 4<BR>\n" );
document.write( "b = +8<BR>\n" );
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document.write( "The equation: h(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F75 ALIGN=MIDDLE  ALT=\"-1%2F75\"   DISABLED_style= \"max-width:90%; height:auto;\" >x^2 + 8x<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+-200%2C+800%2C+-300%2C+1500%2C+%28-1%2F75%29x%5E2%2B8x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-200%2C+800%2C+-300%2C+1500%2C+%28-1%2F75%29x%5E2%2B8x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see the vertex, x=300, y=1200  </SPAN>\n" );
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