document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=406287>Question 406287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, and directrix without completing the square, and deteremine opens upward or downward.<BR>\n" );
document.write( "y=-1/2x sq -3x +2<BR>\n" );
document.write( "I've determined it will open downward, but am confused on how to get the rest of the answers.... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #286866 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=286866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=-1/2x sq -3x +2\r<BR>\n" );
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document.write( "If you do not complete the square to solve, you can use another method using the formula, x-coordinate of the vertex=-b/2a.<BR>\n" );
document.write( "In the given equation, a=-(1/2), b=-3<BR>\n" );
document.write( "x=-(-3)/2(-1/2)=3/-1=-3<BR>\n" );
document.write( "solving for y=-(1/2)(-3)^2 -3(-3) +2<BR>\n" );
document.write( "y=-9/2+9+2=13/2<BR>\n" );
document.write( "This is a parabola that opens downward.<BR>\n" );
document.write( "Coordinates of the vertex are (-3,13/2)<BR>\n" );
document.write( "Axis of symmetry, x=-3<BR>\n" );
document.write( "Set x=0 to find the y-intercept=2<BR>\n" );
document.write( "Set y=0 and solve for x-intercepts by factoring or by using the quadratic formula.<BR>\n" );
document.write( "x=[-(-3)+-sqrt(3^2-4(-1/2)(2)]2*(-1/2)<BR>\n" );
document.write( "x=(3+sqrt(13)/-1 or (3-sqrt(13)/-1<BR>\n" );
document.write( "x=-6.6 or x=.61<BR>\n" );
document.write( "see the graph below of the given equation<BR>\n" );
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