document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117607>Question 117607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the quadratic equation in vertex form.  What is the vertex?  <BR>\n" );
document.write( "y=3x^2+30x+68 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85588 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=85588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the quadratic equation in vertex form.  What is the vertex?  <BR>\n" );
document.write( "y=3x^2+30x+68<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "This equation graphs as a parabola; it has a highest point or<BR>\n" );
document.write( "a lowest point which is called the vertex.<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Put the equation in vertex form by completing the square on the x-terms.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "3(x^2+10x +?) = y-68+3*?<BR>\n" );
document.write( "3(x^2+10x+5^2) = y-68+3*25<BR>\n" );
document.write( "3(x+5)^2 = y+7<BR>\n" );
document.write( "3(x+5)^2 = (y+7)<BR>\n" );
document.write( "(x+5)^2 = (1/3)(y+7)<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Vertex at (-5,-7)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C70%2C3x%5E2%2B30x%2B68%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C70%2C3x%5E2%2B30x%2B68%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );