document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=671743>Question 671743</A>: <I><SPAN STYLE=\"word-break: break-all;\">    Suppose a parabola has vertex (5, –3) and also passes through the point (6, 1). Write the equation of the parabola in vertex form.<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 #417587 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=417587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The parabola can open either up, down, left or right. The problem is, the parabola that opens left or right is not a function as it fails the Vertical Line Test.\r<BR>\n" );
document.write( "\n" );
document.write( "The two vertex-forms of a parabola are:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k=1%2F4p%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k=1%2F4p%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3E0 ALIGN=MIDDLE  ALT=\"p%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, parabola opens up. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3C0 ALIGN=MIDDLE  ALT=\"p%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, parabola opens down.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-h=1%2F4p%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"x-h=1%2F4p%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >: If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3E0 ALIGN=MIDDLE  ALT=\"p%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, parabola opens right. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3C0 ALIGN=MIDDLE  ALT=\"p%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, parabola opens left.\r<BR>\n" );
document.write( "\n" );
document.write( "Sometimes, a substitutes for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4p ALIGN=MIDDLE  ALT=\"1%2F4p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "So, either equations work. The only differences are: one is a function and one is not. One opens down and other opens left.\r<BR>\n" );
document.write( "\n" );
document.write( "The first formula is more precise, as you can find the coordinates of the focus and the equation of the directrix.\r<BR>\n" );
document.write( "\n" );
document.write( "if vertex (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and also passes through the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1 ALIGN=MIDDLE  ALT=\"+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), then we have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-k=%281%2F4%29p%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"y-k=%281%2F4%29p%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B3=%281%2F4%29p%286-5%29%5E2 ALIGN=MIDDLE  ALT=\"1%2B3=%281%2F4%29p%286-5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=%281%2F4%29p%281%29%5E2 ALIGN=MIDDLE  ALT=\"4=%281%2F4%29p%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=%281%2F4%29p%2A1 ALIGN=MIDDLE  ALT=\"4=%281%2F4%29p%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%281%2F4%29=p ALIGN=MIDDLE  ALT=\"4%2F%281%2F4%29=p\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=p ALIGN=MIDDLE  ALT=\"16=p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%3E0 ALIGN=MIDDLE  ALT=\"p%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, parabola opens up\r<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=p ALIGN=MIDDLE  ALT=\"16=p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%281%2F4%29p=%281%2F4%2916=4 ALIGN=MIDDLE  ALT=\"a=%281%2F4%29p=%281%2F4%2916=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, we have:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3=4%28x%5E2-10x%2B25%29 ALIGN=MIDDLE  ALT=\"y%2B3=4%28x%5E2-10x%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3=4x%5E2-40x%2B100 ALIGN=MIDDLE  ALT=\"y%2B3=4x%5E2-40x%2B100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4x%5E2-40x%2B97 ALIGN=MIDDLE  ALT=\"y=4x%5E2-40x%2B97\"   DISABLED_style= \"max-width:90%; height:auto;\" >....your equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Ccircle%286%2C1%2C0.2%29%2Ccircle%285%2C-3%2C0.2%29%2Cgraph%28600%2C600%2C-10%2C10%2C-10%2C10%2C4x%5E2-40x%2B97%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );