document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=238389>Question 238389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you tell me how to convert a parabola into an equation... x intercepts are (3,0) and (13,0) how do i find the vertex if thats all the info i have... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175171 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=175171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x-intercepts are (3,0) and (13,0)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the roots of your equation are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 3<BR>\n" );
document.write( "x = 13\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this was derived from:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x-3 = 0<BR>\n" );
document.write( "x - 13 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that came from:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-3) * (x-13) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply these factors together to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 - 16x + 39 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your quadratic equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it's in standard form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can find the vertex from that form by doing the following:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard form of a quadratic equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ax^2 + bx + c = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 - 16x + 39 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -16<BR>\n" );
document.write( "c = 39\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x value of the vertex is given by the equation x = -b/2a.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 16/2 = 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y value of the vertex is given by the equation y = f(-b/2a).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means y = f(8) which means you replace x with 8 in your equation and solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation is y = x^2 - 16x + 39\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with 8 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 64 - 128 + 39 = -25.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your vertex is (x,y) = (8,-25)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a graph of your equation looks like:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-30%2C30%2C-30%2C30%2Cx%5E2+-+16x+%2B+39%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-30%2C30%2C-30%2C30%2Cx%5E2+-+16x+%2B+39%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are really just working backwards.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given the equation, you find the roots.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are given the roots, you find the equation by backtracking how you find the roots.\r<BR>\n" );
document.write( "<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" );