document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333583>Question 333583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble finding the Vertex of the quadratic equation of <BR>\n" );
document.write( "-0.2x^2 + 12x + 11 = 0<BR>\n" );
document.write( "I have worked it to find that it has two solutions that being x = -0.90307428 and x = 60.90307428. <BR>\n" );
document.write( "I am confused at how to find the vertex of the curve. <BR>\n" );
document.write( "Thanks for any help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #239073 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=239073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your quadratic equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2+%2B+12x+%2B+11 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2+%2B+12x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "the vertex can be found where  x=-b/(2a) this comes from the quadratic solution for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-0.2x%5E2+%2B+12x+%2B+11 ALIGN=MIDDLE  ALT=\"0=-0.2x%5E2+%2B+12x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > and its the front part of the quadratic solution.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "so vertex (x,y) is where  x=-b/(2a) and substituting this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2+%2B+12x+%2B+11 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2+%2B+12x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to get the y part.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2+%2B+12x+%2B+11 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2+%2B+12x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=-0.2, b=12, c=11<BR>\n" );
document.write( "--<BR>\n" );
document.write( "x=-b/(2a)= -12/(2*(-0.2))=30<BR>\n" );
document.write( "y=-0.2*30^2 +12(30)+11 = -180+360+11=191<BR>\n" );
document.write( "vertex = (30,191)<BR>\n" );
document.write( "===<BR>\n" );
document.write( "you could have also worked <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2+%2B+12x+%2B+11 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2+%2B+12x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "into the form  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=d%2A%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=d%2A%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > by completing the square and in this form<BR>\n" );
document.write( "the vertex would have been (h,k)\r<BR>\n" );
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