document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57272>Question 57272</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534400329/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> We are asked to graph the following quadradic equation -f(x)=X^2-3x+1.\r<BR>\n" );
document.write( "\n" );
document.write( "AS I graph it the parabola opens up, 3 spaces up and is moved over 1 space to the right.  However according to the book it opens down and over 1 and up the y-axis 3 spaces.  If X^2 is positive I thought it opened up?!?! where am I going wrong or what do I not understand??  Any help will be appreciated on this.\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38980 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=38980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -f(x)=X^2-3x+1. <BR>\n" );
document.write( "You are given the formula for negative f(x)<BR>\n" );
document.write( "If you multiply each side by minus-one you<BR>\n" );
document.write( "will get:<BR>\n" );
document.write( "f(x)=-x^2+3x+1<BR>\n" );
document.write( "Now you should see that it opens down because<BR>\n" );
document.write( "of the negative coefficient of x^2<BR>\n" );
document.write( "If you complete the square you get:<BR>\n" );
document.write( "y-1+?=-(x^2-3x+?<BR>\n" );
document.write( "y-1-(3/2)^2=-(x^2-3x+(3/2)^2)<BR>\n" );
document.write( "y-(13/4)=-(x-(3/2))^2<BR>\n" );
document.write( "So the vertex is at (3/2,13,4)<BR>\n" );
document.write( "Hope this helps.<BR>\n" );
document.write( "cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );