document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=108951>Question 108951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem:<BR>\n" );
document.write( "f(x)=-4x^2+ 4x-1\r<BR>\n" );
document.write( "\n" );
document.write( "This is what the problem asks:<BR>\n" );
document.write( "a)use the quad formula to find zeros<BR>\n" );
document.write( "b)Find Max or min value<BR>\n" );
document.write( "c)sketch the graph\r<BR>\n" );
document.write( "\n" );
document.write( "This is what I have done so far:<BR>\n" );
document.write( "-4+/- sqr rt(4^2-4(-4)(-1))/2(-4)\r<BR>\n" );
document.write( "\n" );
document.write( "Note: This should be set up using the quad formula\r<BR>\n" );
document.write( "\n" );
document.write( "This is what I came up with:\r<BR>\n" );
document.write( "\n" );
document.write( "x= -4+/- sqrt(16-16)/ -8\r<BR>\n" );
document.write( "\n" );
document.write( "Note: also set up in quad formula.\r<BR>\n" );
document.write( "\n" );
document.write( "My problen is what to to with the 16s. If I subtract them that leaves Zero. I'm stuck here. I can look at the equation and tell it will be a max value but what are the zeros? Please help?<BR>\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 #79443 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=79443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are correct so far.  The sqrt(16 - 16) is zero. If you replace it with zero in your equation<BR>\n" );
document.write( "for x you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4%2B-0%29%2F-8+=+%28-4%29%2F%28-8%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-4%2B-0%29%2F-8+=+%28-4%29%2F%28-8%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And you are further correct that this graph rises to a peak and then drops back down.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This means that you only have one zero and it occurs when x is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the graph<BR>\n" );
document.write( "just touches the x-axis at its peak and that \"touching\" is at the value x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And at this point the maximum value is y = 0.  The graph looks like this:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-10%2C2%2C-4x%5E2%2B4x-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-10%2C2%2C-4x%5E2%2B4x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "You did everything correctly, but just didn't recognize how to interpret your answer. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to see how to view answers when the terms in the radical reduce to zero.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );