document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110904>Question 110904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the graph, what are the solution(s) to the equation -x2+4x+5=0<BR>\n" );
document.write( "That is x squared<BR>\n" );
document.write( "Does this function have a maximum or a minimum?<BR>\n" );
document.write( "What are the coordinates of the vertex in (x, y) form?<BR>\n" );
document.write( "What is the equation of the line of symmetry for this graph? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80951 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=80951\">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=-x%5E2+%2B+4x+%2B+5+=+0 ALIGN=MIDDLE  ALT=\"-x%5E2+%2B+4x+%2B+5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The quadratic formula for this is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where<BR>\n" );
document.write( "a = -1<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "c = 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A%28-1%29%2A5+%29%29%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A%28-1%29%2A5+%29%29%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+4%5E2+%2B+20+%29%29%2F-2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+4%5E2+%2B+20+%29%29%2F-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The +-sqrt(-) part is the + distance of one root from the axis of <BR>\n" );
document.write( "symmetry and the - distance of the other root from the axis of symmetry.<BR>\n" );
document.write( "So, the axis is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-4+%2F+-2+ ALIGN=MIDDLE  ALT=\"x+=+-4+%2F+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer: equation of axis of symmetry<BR>\n" );
document.write( "If I plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the original equation, I'll get the y-coordinate of the vertex<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2+%2B+4x+%2B+5+ ALIGN=MIDDLE  ALT=\"y+=+-x%5E2+%2B+4x+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-4+%2B+8+%2B+5+ ALIGN=MIDDLE  ALT=\"y+=+-4+%2B+8+%2B+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9 ALIGN=MIDDLE  ALT=\"y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "coordinates of vertex: (2,9)<BR>\n" );
document.write( "The roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"0+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from Axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2B-+sqrt%28+16+%2B+20+%29%29%2F-2%29+ ALIGN=MIDDLE  ALT=\"0%2B-+sqrt%28+16+%2B+20+%29%29%2F-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B+6%2F-2 ALIGN=MIDDLE  ALT=\"%2B+6%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+6%2F-2 ALIGN=MIDDLE  ALT=\"-+6%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B3 ALIGN=MIDDLE  ALT=\"%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > on either side of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer: solutions to equation<BR>\n" );
document.write( "Looking at the 3 points, V(2,9), (-1,0) and (5,0), The vertex is <BR>\n" );
document.write( "above the solution points, so the parabola curves downward. the<BR>\n" );
document.write( "vertex is a maximum answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );