document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=485722>Question 485722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I needed help with my precalc honors summer work, and I was wondering if someone could help me. How do I:<BR>\n" );
document.write( "a) Express the quadratic equation in standard form<BR>\n" );
document.write( "b) Sketch the graph (I know how do do this)<BR>\n" );
document.write( "c) Find its maximum or minimum value (What does this mean? The vertex?)<BR>\n" );
document.write( "What I have so far:<BR>\n" );
document.write( "Original equation: f(x)=2x-x^2<BR>\n" );
document.write( "A)<BR>\n" );
document.write( "f(x)=2x-x^2<BR>\n" );
document.write( "     -x^2+2x+0<BR>\n" );
document.write( "     (-x^2+2x+1)-1<BR>\n" );
document.write( "     -(x^2-2x-1)+1<BR>\n" );
document.write( "I got stuck...I would love it if someone would explain to me how to get rid of the negative coefficient so I can factor it, and how to put this equation into standard form. Also I would appreciate it a ton if someone could tell me what minimum/maximum of a graph is and how to find it. Thanks a ton, Jess </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332691 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=332691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Express the quadratic equation in standard form<BR>\n" );
document.write( "b) Sketch the graph (I know how do do this)<BR>\n" );
document.write( "c) Find its maximum or minimum value (What does this mean? The vertex?)<BR>\n" );
document.write( "What I have so far:<BR>\n" );
document.write( "Original equation: f(x)=2x-x^2<BR>\n" );
document.write( "**<BR>\n" );
document.write( "a) Quadratic equations are parabolas of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. <BR>\n" );
document.write( "For given equation: <BR>\n" );
document.write( "y=-x^2+2x<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "y=-(x^2-2x+1)+1<BR>\n" );
document.write( "y=-(x-1)^2+1<BR>\n" );
document.write( "vertex: (1,1)<BR>\n" );
document.write( "The negative sign of the lead coefficient means that the parabola opens downwards, that is, it has a maximum value=1 (y-coordinate of vertex)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "see graph below as a visual check on the answers:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C-x%5E2%2B2x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C-x%5E2%2B2x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );