document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195875>Question 1195875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a ball is thrown or kicked, the path it travels is shaped like a parabola. Suppose a football is kicked from ground level, reaches a maximum height of 20 feet, and hits the ground 120 feet from where it was kicked. Assuming that the ball was kicked at the origin, write an equation of the parabola that models the flight of the ball.<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 #828468 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=828468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Finding the equation using standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > and using the three known points to form a system of three equations in a, b, and c is one way to get the answer.<br><BR>\n" );
document.write( "Usually an easier way, when the vertex of the parabola is known, is to use the vertex form of the equation of a parabola:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k=a%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k=a%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Knowing the points (0,0), (60,20), and (120,0), we know the vertex is (60,20).  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-20=a%28x-60%29%5E2 ALIGN=MIDDLE  ALT=\"y-20=a%28x-60%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use either of the other two points to determine the constant a.  Using (0,0)...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-20=a%280-60%29%5E2 ALIGN=MIDDLE  ALT=\"0-20=a%280-60%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20=a%283600%29 ALIGN=MIDDLE  ALT=\"-20=a%283600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-20%2F3600=-1%2F180 ALIGN=MIDDLE  ALT=\"a=-20%2F3600=-1%2F180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-20=%28-1%2F180%29%28x-60%29%5E2 ALIGN=MIDDLE  ALT=\"y-20=%28-1%2F180%29%28x-60%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then manipulate that equation to put it in the required form, if necessary.<br><BR>\n" );
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