document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131569>Question 1131569</A>: <I><SPAN STYLE=\"word-break: break-all;\"> FIND EQUATION OF A PARABOLA WITH FOCAL WIDTH OF 8, AXIS PARALLEL TO Y AXIS, PASSING THROUGH (5,0) AND (9,-6. THANK YOU IN ADVANCE... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748262 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13334)</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=748262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If you use this form of the equation for a parabola<br><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( "Then the vertex is (h,k) and the focal width is 4p.<br><BR>\n" );
document.write( "So with the two given points on the parabola, and knowing the focal width is 8, we get two equations in h and k:<br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%281%2F8%29%285-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"0+=+%281%2F8%29%285-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%281%2F8%29%28h%5E2-10h%2B25%29%2Bk ALIGN=MIDDLE  ALT=\"0+=+%281%2F8%29%28h%5E2-10h%2B25%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+%281%2F8%29%289-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"6+=+%281%2F8%29%289-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+%281%2F8%29%28h%5E2-18h%2B81%29%2Bk ALIGN=MIDDLE  ALT=\"6+=+%281%2F8%29%28h%5E2-18h%2B81%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Subtracting (1) from (2) eliminates k:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+%281%2F8%29%28-8h%2B56%29 ALIGN=MIDDLE  ALT=\"6+=+%281%2F8%29%28-8h%2B56%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8h%2B56+=+48 ALIGN=MIDDLE  ALT=\"-8h%2B56+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8h+=+-8 ALIGN=MIDDLE  ALT=\"-8h+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+1 ALIGN=MIDDLE  ALT=\"h+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substituting h=1 in (1) gives us k:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%281%2F8%29%285-1%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"0+=+%281%2F8%29%285-1%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2%2Bk ALIGN=MIDDLE  ALT=\"0+=+2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-2 ALIGN=MIDDLE  ALT=\"k+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: An equation of the given parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F8%29%28x-1%29%5E2-2 ALIGN=MIDDLE  ALT=\"y+=+%281%2F8%29%28x-1%29%5E2-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph....  The vertex is (h,k) = (1,-2).  p=2 is the distance from the vertex to the focus, so the focus is (1,0); so you can see in the graph that the focal width is 8, with the parabola having x-intercepts -3 and 5.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C280%2C-10%2C10%2C-4%2C10%2C%281%2F8%29%28x-1%29%5E2-2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C280%2C-10%2C10%2C-4%2C10%2C%281%2F8%29%28x-1%29%5E2-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );