document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176694>Question 1176694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Vertex (1,3); passing through (2,6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803907 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=803907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Recall that <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "represents the generalized vertex form. <BR>\n" );
document.write( "a = leading coefficient<BR>\n" );
document.write( "h = x coordinate of vertex<BR>\n" );
document.write( "k = y coordinate of vertex\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since the vertex given to us is (1,3), this means (h,k) = (1,3)<BR>\n" );
document.write( "In other words,<BR>\n" );
document.write( "h = 1<BR>\n" );
document.write( "k = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're also told the parabola passes through (x,y) = (2,6)<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "y = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have these four items of info<BR>\n" );
document.write( "h = 1<BR>\n" );
document.write( "k = 3<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "y = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Plug those four items into the first equation mentioned and isolate 'a'.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+a%282-1%29%5E2+%2B+3 ALIGN=MIDDLE  ALT=\"6+=+a%282-1%29%5E2+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+a%281%29%5E2+%2B+3 ALIGN=MIDDLE  ALT=\"6+=+a%281%29%5E2+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+a+%2B+3 ALIGN=MIDDLE  ALT=\"6+=+a+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-3+=+a ALIGN=MIDDLE  ALT=\"6-3+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+a ALIGN=MIDDLE  ALT=\"3+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+3 ALIGN=MIDDLE  ALT=\"a+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The leading coefficient is positive, so the parabola opens upward.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E2+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E2+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "turn into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%28x-1%29%5E2+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+3%28x-1%29%5E2+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "after plugging in a = 3, h = 1, k = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We could expand things out and combine like terms like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%28x-1%29%5E2+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+3%28x-1%29%5E2+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%28x%5E2-2x%2B1%29+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+3%28x%5E2-2x%2B1%29+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL rule\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x%5E2-6x%2B3+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+3x%5E2-6x%2B3+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"y+=+3x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%28x-1%29%5E2+%2B+3 ALIGN=MIDDLE  ALT=\"y+=+3%28x-1%29%5E2+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > expands and simplifies to the standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x%5E2-6x%2B9 ALIGN=MIDDLE  ALT=\"y+=+3x%5E2-6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+0%2C3%28x-1%29%5E2+%2B+3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+0%2C3%28x-1%29%5E2+%2B+3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "note the vertex is the lowest point at (1,3)<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );