document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=312004>Question 312004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm so lost with this. Please help!!!<BR>\n" );
document.write( " find the vertex. f(x)= 5(x+ 1/4)^2+19\r<BR>\n" );
document.write( "\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 #223077 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20086)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=223077\">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=%22f%28x%29%22=+5%28x%2B+1%2F4%29%5E2%2B19 ALIGN=MIDDLE  ALT=\"%22f%28x%29%22=+5%28x%2B+1%2F4%29%5E2%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "You must memorize the standard equation of a parabola, which is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22f%28x%29%22=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"%22f%28x%29%22=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "learn how to compare your equation with that:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22f%28x%29%22=+5%28x%2B+1%2F4%29%5E2%2B19 ALIGN=MIDDLE  ALT=\"%22f%28x%29%22=+5%28x%2B+1%2F4%29%5E2%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "And see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-1%2F4 ALIGN=MIDDLE  ALT=\"h=-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=19 ALIGN=MIDDLE  ALT=\"k=19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "You must also learn that the vertex is the point (h,k), which is\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28%22 ALIGN=MIDDLE  ALT=\"%22%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2C%22 ALIGN=MIDDLE  ALT=\"%22%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19 ALIGN=MIDDLE  ALT=\"19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%29%22 ALIGN=MIDDLE  ALT=\"%22%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and that since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a positive number,<BR>\n" );
document.write( "the graph opens upward.\r<BR>\n" );
document.write( "\n" );
document.write( "To check:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22f%28x%29%22 ALIGN=MIDDLE  ALT=\"%22f%28x%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > means the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so find<BR>\n" );
document.write( "some points for:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+5%28x%2B+1%2F4%29%5E2%2B19 ALIGN=MIDDLE  ALT=\"y=+5%28x%2B+1%2F4%29%5E2%2B19\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "substitute x=-4, get y=89.3<BR>\n" );
document.write( "substitute x=-3, get y=56.3<BR>\n" );
document.write( "substitute x=-2, get y=34.3<BR>\n" );
document.write( "substitute x=-1, get y=21.8<BR>\n" );
document.write( "substitute x=0, get y=19.3<BR>\n" );
document.write( "substitute x=1, get y=28.8<BR>\n" );
document.write( "substitute x=2, get y=44.3<BR>\n" );
document.write( "substitute x=3, get y=71.8<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-4%2C4%2C-100%2C100%2C+5%28x%2B1%2F4%29%5E2%2B19%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-4%2C4%2C-100%2C100%2C+5%28x%2B1%2F4%29%5E2%2B19%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "And it looks like the graph of its vertex (turning point) is:\r<BR>\n" );
document.write( "\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28%22 ALIGN=MIDDLE  ALT=\"%22%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%2C%22 ALIGN=MIDDLE  ALT=\"%22%2C%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19 ALIGN=MIDDLE  ALT=\"19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%29%22 ALIGN=MIDDLE  ALT=\"%22%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Edwin</pre> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );