document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=408222>Question 408222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the vertex formula to find the vertex<BR>\n" );
document.write( "find the intervals where f is increasing and where f is decreasing\r<BR>\n" );
document.write( "\n" );
document.write( "f(x)=2x^2-4x+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287660 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=287660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E2-4x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E2-4x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The vertex is found using the formula for (x,y):\r<BR>\n" );
document.write( "\n" );
document.write( "(-b/2a,f(-b/2a))\r<BR>\n" );
document.write( "\n" );
document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=x=-b%2F2a=-%28-4%29%2F2%2A2=4%2F4=1 ALIGN=MIDDLE  ALT=\"x=-b%2F2a=-%28-4%29%2F2%2A2=4%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...so we have (1,y)..now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=f%28-b%2F2a%29 ALIGN=MIDDLE  ALT=\"y=f%28-b%2F2a%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=f%281%29=2%2A1%5E2-4%2A1%2B1 ALIGN=MIDDLE  ALT=\"f%281%29=2%2A1%5E2-4%2A1%2B1\"   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=f%281%29=2-4%2B1 ALIGN=MIDDLE  ALT=\"f%281%29=2-4%2B1\"   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=f%281%29=-1 ALIGN=MIDDLE  ALT=\"f%281%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >................ so  the vertex is  (1,-1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the intervals on which the function is increasing and the intervals on which the function is decreasing\r<BR>\n" );
document.write( "\n" );
document.write( "Given the vertex of (1,-1):\r<BR>\n" );
document.write( "\n" );
document.write( "The function is decreasing on:\r<BR>\n" );
document.write( "\n" );
document.write( "(-&#8734;,1)\r<BR>\n" );
document.write( "\n" );
document.write( "The function is increasing  on:\r<BR>\n" );
document.write( "\n" );
document.write( "(1,&#8734;)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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+2x%5E2-4x%2B1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+2x%5E2-4x%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );