document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159758>Question 1159758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=x^2+6x+3 What is the axis of symmetry? x=x= Compute the coordinates of the vertex: (( , )) compute the yy-intercept as a point: (( , )) find the point symmetric to the yy-intercept </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782825 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=782825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Put the equation in vertex form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In that form, the vertex is at (h,k), and the axis of symmetry is x=h.<br><BR>\n" );
document.write( "Complete the square....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B3+=+%28x%5E2%2B6x%2B9%29%2B3-9+=+%28x%2B3%29%5E2-6 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B3+=+%28x%5E2%2B6x%2B9%29%2B3-9+=+%28x%2B3%29%5E2-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This form of the equation tells us that the vertex is at (-3,-6) and the axis of symmetry is x=-3.  That can be seen in the graph:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B6x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B6x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For the y-intercept, set x=0 and evaluate.  Using the given form of the equation, it is easy to see that the y-intercept is (0,3).<br><BR>\n" );
document.write( "The y-intercept is 3 units to the right of the axis of symmetry; the point symmetric with the y-intercept will be 3 units to the left of the axis of symmetry, and it will have the same y value as the y-intercept: (-6,3).  That is also easily seen in the graph.<br><BR>\n" );
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