document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=201029>Question 201029</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the mamium value of the function y=-x^2+3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151264 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=151264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I don't know what a \"mamim\" [sic] value is.  However, since the graph of this function is a parabola opening downward, it does have a maximum value.  I'll go out on a limb and presume that is what you meant to ask.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You know the graph opens downward because the lead coefficient is negative, therefore the value of the function at the vertex of the parabola is the maximum value of the function.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For any function <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = ax^2 + bx + c\">, the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex is found by calculating:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{-b}{2a}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then the maximum value of the function is found by substituting the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> in the function and then calculating the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">.  Note that the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\"> in your given function is zero because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -x^2 + 3 = -x^2 + 0x + 3\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28%0D%0A500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A-x%5E2%2B3%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "By the way, just on the off chance that my opening remarks caused you to roll your eyes and say \"WHAT-<i>ever</i>\", think about this:  The <i>only</i> way that we can communicate on this system is in writing using the English language.  Therefore, all of the niceties of correct spelling, grammar, syntax, and punctuation, as well as the strict definition of mathematical vocabulary must be observed in order to ensure that communication is consistently effective.  Besides, writing correctly is a polite gesture of respect to those of us who volunteer our time to help you.  Inattention to such details sends just the opposite message.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );