document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725980>Question 725980</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the quadratic function whose graph passes through the point (-1,3)   and has vertex (2,-4)  .<BR>\n" );
document.write( "  ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444409 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=444409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If equation has the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "then the x co-ordinate of the vertex is at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bv%5D+=+-b%2F%28a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bv%5D+=+-b%2F%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given: vertex at (2,-4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+2+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b+=+4a+ ALIGN=MIDDLE  ALT=\"+-b+=+4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4a+ ALIGN=MIDDLE  ALT=\"+b+=+-4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "also:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4+=+a%2Ax%5E2+-+4a%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+-4+=+a%2Ax%5E2+-+4a%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4+=+a%2A2%5E2+-+4a%2A2+%2B+c+ ALIGN=MIDDLE  ALT=\"+-4+=+a%2A2%5E2+-+4a%2A2+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4+=+4a+-+8a+%2B+c%0D%0A%7B%7B%7B+-4a+%2B+c+=+-4+ ALIGN=MIDDLE  ALT=\"+-4+=+4a+-+8a+%2B+c%0D%0A%7B%7B%7B+-4a+%2B+c+=+-4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+-+c+=+4+ ALIGN=MIDDLE  ALT=\"+4a+-+c+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Also given: (-1,3) is a solution<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+a%2A%28-1%29%5E2+-+4a%2A%28-1%29+%2B+c+ ALIGN=MIDDLE  ALT=\"+3+=+a%2A%28-1%29%5E2+-+4a%2A%28-1%29+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+a+%2B+4a+%2B+c+ ALIGN=MIDDLE  ALT=\"+3+=+a+%2B+4a+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+%2B+c+=+3+ ALIGN=MIDDLE  ALT=\"+5a+%2B+c+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Add (1) and (2)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4a+-+c+=+4+ ALIGN=MIDDLE  ALT=\"+4a+-+c+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+%2B+c+=+3+ ALIGN=MIDDLE  ALT=\"+5a+%2B+c+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9a+=+7+ ALIGN=MIDDLE  ALT=\"+9a+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+7%2F9+ ALIGN=MIDDLE  ALT=\"+a+=+7%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4a+ ALIGN=MIDDLE  ALT=\"+b+=+-4a+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-4%2A%287%2F9%29+ ALIGN=MIDDLE  ALT=\"+b+=+-4%2A%287%2F9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-28%2F9+ ALIGN=MIDDLE  ALT=\"+b+=+-28%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "also<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5a+%2B+c+=+3+ ALIGN=MIDDLE  ALT=\"+5a+%2B+c+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+35%2F9+%2B+c+=+3+ ALIGN=MIDDLE  ALT=\"+35%2F9+%2B+c+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+27%2F9+-+35%2F9+ ALIGN=MIDDLE  ALT=\"+c+=+27%2F9+-+35%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-8%2F9+ ALIGN=MIDDLE  ALT=\"+c+=+-8%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%287%2F9%29%2Ax%5E2+-+%2828%2F9%29%2Ax+-+8%2F9+ ALIGN=MIDDLE  ALT=\"+y+=+%287%2F9%29%2Ax%5E2+-+%2828%2F9%29%2Ax+-+8%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "check: is the vertex at (2,-4) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+2+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2828%2F9%29+%2F+%282%2A%287%2F9%29%29+=+2+ ALIGN=MIDDLE  ALT=\"+%2828%2F9%29+%2F+%282%2A%287%2F9%29%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2828%2F9%29%2A%289%2F14%29+=+2+ ALIGN=MIDDLE  ALT=\"+%2828%2F9%29%2A%289%2F14%29+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+=+2+ ALIGN=MIDDLE  ALT=\"+2+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4+=+%287%2F9%29%2A4+-+%2828%2F9%29%2A2+-+8%2F9+ ALIGN=MIDDLE  ALT=\"+-4+=+%287%2F9%29%2A4+-+%2828%2F9%29%2A2+-+8%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4+=+28%2F9+-+56%2F9+-+8%2F9+ ALIGN=MIDDLE  ALT=\"+-4+=+28%2F9+-+56%2F9+-+8%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-36+=+28+-56+-8+ ALIGN=MIDDLE  ALT=\"+-36+=+28+-56+-8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-36+=+-36+ ALIGN=MIDDLE  ALT=\"+-36+=+-36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Does it go through (-1,3) ?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%287%2F9%29%2Ax%5E2+-+%2828%2F9%29%2Ax+-+8%2F9+ ALIGN=MIDDLE  ALT=\"+y+=+%287%2F9%29%2Ax%5E2+-+%2828%2F9%29%2Ax+-+8%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+%287%2F9%29%2A%28-1%29%5E2+-+%2828%2F9%29%2A%28-1%29+-+8%2F9+ ALIGN=MIDDLE  ALT=\"+3+=+%287%2F9%29%2A%28-1%29%5E2+-+%2828%2F9%29%2A%28-1%29+-+8%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+=+7%2F9+%2B+28%2F9+-+8%2F9+ ALIGN=MIDDLE  ALT=\"+3+=+7%2F9+%2B+28%2F9+-+8%2F9+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27+=+7+%2B+28+-+8+ ALIGN=MIDDLE  ALT=\"+27+=+7+%2B+28+-+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+27+=+27+ ALIGN=MIDDLE  ALT=\"+27+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );