document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166292>Question 1166292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 1 and 2, do the following:<BR>\n" );
document.write( "	a)  Write the equation of the parabola in standard form.<BR>\n" );
document.write( "	b)  Find the vertex, focus, equation of the directrix and axis of symmetry of the parabola.<BR>\n" );
document.write( "1.  x^2-6x-5y-1=0<BR>\n" );
document.write( "2.  y^2-2y+3x-8=0\r<BR>\n" );
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document.write( "In 3 and 4, find an equation of the parabola that satisfies the given conditions.  Express the answer in standard and general forms.<BR>\n" );
document.write( "3.  Vertex at V(-4,3),directrix at y=5.<BR>\n" );
document.write( "4.  Focus at F(-1,-5),directrix at x=-2.\r<BR>\n" );
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document.write( "5.  Each cable of a suspension bridge is in the shape of a parabola and is supported by two towers at each end (refer to the figure below).  The shape of the cable is modeled by the equation <BR>\n" );
document.write( "				x^2=200y<BR>\n" );
document.write( "where x and y are measured in meters.  Find the coordinates of the focus.\r<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 #790795 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=790795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "One problem per post!!!<br><BR>\n" );
document.write( "Here is all you need to work these problems yourself....<br><BR>\n" );
document.write( "Vertex form of equation of a parabola that opens up or down:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k=%281%2F%284p%29%29%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k=%281%2F%284p%29%29%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F%284p%29%29%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y+=+%281%2F%284p%29%29%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Vertex form of equation of a parabola that opens right or left:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-h=%281%2F%284p%29%29%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"x-h=%281%2F%284p%29%29%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F%284p%29%29%28y-k%29%5E2%2Bh ALIGN=MIDDLE  ALT=\"x+=+%281%2F%284p%29%29%28y-k%29%5E2%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In both formulas, the vertex is (h,k), and p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br><BR>\n" );
document.write( "Here is a problem like your problems 1 and 2....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B4y=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B4y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Complete the square in x and put the equation in vertex form.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4x%2B4%29%2B4y-4+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2-4x%2B4%29%2B4y-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B4y-4=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B4y-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y-4=%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"4y-4=%28x-2%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=4%28y-4%29=%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"4%28y-4%29=%28x-2%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=y-4=%281%2F4%29%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"y-4=%281%2F4%29%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That is vertex form: h=2; k=4; 4p=4 so p=1.<br><BR>\n" );
document.write( "The vertex is (h,k) = (2,4).<br><BR>\n" );
document.write( "p=1, so the directed distance from the directrix to the vertex is 1, and the directed distance from the vertex to the focus is 1.  That makes the directrix y=3 and the focus (2,5).<br><BR>\n" );
document.write( "Your problem 5 is solved in a similar fashion.<br><BR>\n" );
document.write( "For problems 3 and 4, use the definitions of (h,k) and p to write the equations.<br><BR>\n" );
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