document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=447407>Question 447407</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A gound base missile is launched from the origin (0,0), it reaches a maximum height of 10km and lands 200km away at the point (200,0) determine the quadratic equation. The missiles flight path is a parabola. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308133 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=308133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A gound base missile is launched from the origin (0,0), <BR>\n" );
document.write( "it reaches a maximum height of 10km and lands 200km away at the point (200,0)<BR>\n" );
document.write( " determine the quadratic equation. The missiles flight path is a parabola.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The max height is halfway between launch and impact point: 100 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Two ordered pairs: 100, 10 and 200, 0<BR>\n" );
document.write( "Using the form ax^2 + bx + c = y; c = 0 here so we have:<BR>\n" );
document.write( "100, 10<BR>\n" );
document.write( "100^2*a + 100b = 10<BR>\n" );
document.write( "10000a + 100b = 10<BR>\n" );
document.write( "and<BR>\n" );
document.write( "200, 0<BR>\n" );
document.write( "200^2*a + 200b = 0<BR>\n" );
document.write( "40000a + 200b = 0<BR>\n" );
document.write( "multiply the 1st equation by 2, subtract from the above equation<BR>\n" );
document.write( "40000a + 200b = 0<BR>\n" );
document.write( "20000a + 200b = 20<BR>\n" );
document.write( "---------------------subtraction eliminates b, find a<BR>\n" );
document.write( "20000a = -20<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-20%29%2F%2820000%29 ALIGN=MIDDLE  ALT=\"%28-20%29%2F%2820000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -.001<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find b using the 1st equation<BR>\n" );
document.write( "10000(-.001) + 100b = 10<BR>\n" );
document.write( "-10 + 100b = 10<BR>\n" );
document.write( "100b = 10 + 10<BR>\n" );
document.write( "100b = 20<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F100 ALIGN=MIDDLE  ALT=\"20%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = .2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The equation: y = -.001x^2 + .2x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "looks like this;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-50%2C+250%2C+-6%2C+12%2C+-.001x%5E2%2B.2x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-50%2C+250%2C+-6%2C+12%2C+-.001x%5E2%2B.2x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );