document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980100>Question 980100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A projectile follows a parabolic path whose height in meters, is given by the function f(x) = -x^2 +2x +2.<BR>\n" );
document.write( "Find the mazimum horizontal distance that the projectile may cover. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601308 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the maximum horizontal distance, which represents x in our quadratic equation, we will need to use the quadratic formula to find x.  \r<BR>\n" );
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document.write( "ax^2 + bx + c -----> -x^2 + 2x + 2\r<BR>\n" );
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document.write( "a = -1<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( "c = 2\r<BR>\n" );
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document.write( "quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+%28-2%2B-sqrt%282%5E2-%284%29%28-1%29%282%29%29%29%2F%282%29%28-1%29 ALIGN=MIDDLE  ALT=\"x=+%28-2%2B-sqrt%282%5E2-%284%29%28-1%29%282%29%29%29%2F%282%29%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -----> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-sqrt%284%2B8%29%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-sqrt%284%2B8%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2+%2B-sqrt%2812%29%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%28-2+%2B-sqrt%2812%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%2B-2sqrt%283%29%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%28-2%2B-2sqrt%283%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-2%281+%2B-sqrt%283%29%29%29%2F-2 ALIGN=MIDDLE  ALT=\"x=%28-2%281+%2B-sqrt%283%29%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2B-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=1%2B-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "We will now disregard the - sign, because if we subtract the square root of 3 from 1, we will obtain a negative number.  A projectile that has not yet moved will start at the point (0,0) on a graph (unless we are told the projectile starts off at a different height, in which case our y coordinate may be higher than 0), so our x coordinate cannot be a negative number.  We only want to find the distance between the original x coordinate (0) and the x coordinate where the projectile lands.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Bsqrt%283%29 ALIGN=MIDDLE  ALT=\"x=1%2Bsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2B1.732 ALIGN=MIDDLE  ALT=\"x=1%2B1.732\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----->\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2.732 ALIGN=MIDDLE  ALT=\"x=2.732\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the maximum horizontal distance that the projectile may cover is approximately 2.732 meters.\r<BR>\n" );
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document.write( "On a graph, the parabola will look like the following (note that the x coordinate where the projectile lands is 2.732)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-1%2C+4%2C+-1%2C+4%2C+-x%5E2+%2B+2x+%2B+2+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+4%2C+-1%2C+4%2C+-x%5E2+%2B+2x+%2B+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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