document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54866>Question 54866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Transform the general equation y=ax^2+bx+c to vertex form.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #37250 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=37250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Transform the general equation y=ax^2+bx+c to vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=a%28x-h%29%5E2%2Bk%29 ALIGN=MIDDLE  ALT=\"highlight%28y=a%28x-h%29%5E2%2Bk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where the vertex=(h,k).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%5E2%2Bbx%2Fa%29%2Bc ALIGN=MIDDLE  ALT=\"y=a%28x%5E2%2Bbx%2Fa%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%5E2%2Bbx%2Fa%2B%28b%2F2a%29%5E2%29-a%28b%2F2a%29%5E2%2Bc ALIGN=MIDDLE  ALT=\"y=a%28x%5E2%2Bbx%2Fa%2B%28b%2F2a%29%5E2%29-a%28b%2F2a%29%5E2%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%2Bb%2F2a%29%5E2-b%5E2%2F4a%2Bc ALIGN=MIDDLE  ALT=\"y=a%28x%2Bb%2F2a%29%5E2-b%5E2%2F4a%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%2Bb%2F2a%29%5E2-b%5E2%2F4a%2B4a%2Fc ALIGN=MIDDLE  ALT=\"y=a%28x%2Bb%2F2a%29%5E2-b%5E2%2F4a%2B4a%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%2Bb%2F2a%29%5E2%2B%28-b%5E2%2B4ac%29%2F4a ALIGN=MIDDLE  ALT=\"y=a%28x%2Bb%2F2a%29%5E2%2B%28-b%5E2%2B4ac%29%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%5E2%2B2bx%2F2a%2Bb%5E2%2F4a%5E2%29%2B%28-b%5E2%2B4ac%29%2F4a ALIGN=MIDDLE  ALT=\"y=a%28x%5E2%2B2bx%2F2a%2Bb%5E2%2F4a%5E2%29%2B%28-b%5E2%2B4ac%29%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2B2abx%2F2a%2Bab%5E2%2F4a%5E2-b%5E2%2F4a%2B4ac%2F4a ALIGN=MIDDLE  ALT=\"y=ax%5E2%2B2abx%2F2a%2Bab%5E2%2F4a%5E2-b%5E2%2F4a%2B4ac%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bb%5E2%2F4a-b%5E2%2F4a%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bb%5E2%2F4a-b%5E2%2F4a%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Keep in mind that this was done by a human, when there are only letters and variables involved, I can only do but so much to check myself.  I checked it against a real quadratic equation in which I could find the vertex.  If I'm right the x value of the vertex would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > (that actually matches the known formula for the x value of the vertex in an equation written in standard form) and the y value would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-b%5E2%2B4ac%29%2F4a%29 ALIGN=MIDDLE  ALT=\"y=%28-b%5E2%2B4ac%29%2F4a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Good Luck!!!<BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
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