document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179671>Question 1179671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the equation, identify the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum values.\r<BR>\n" );
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document.write( "1. y = -2(x - 3) 2  + 9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #809239 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The vertex is at (-h, k), which would be x=3, y=9 or (3, 9)<BR>\n" );
document.write( "The axis of symmetry is therefore at x=3.<BR>\n" );
document.write( "the y-intercept is where x=0, and that is -2(9)+9=-9 so (0, -9)<BR>\n" );
document.write( "The maximum value for this convex upward parabola is when x=3 and that has already been shown to have y=9.<BR>\n" );
document.write( "The minimum values are at -oo.<BR>\n" );
document.write( "For the zeros, let y=0, <BR>\n" );
document.write( "then -2(x-3)^2=-9<BR>\n" );
document.write( "or (x-3)^2=9/2<BR>\n" );
document.write( "x-3=+/- 3(sqrt(2)/2<BR>\n" );
document.write( "so the zeros are 3+/- (3/2) sqrt (2)<BR>\n" );
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document.write( "Can check by writing it in standard form<BR>\n" );
document.write( "y=-2x^2+12x-18+9; -2x^2+12x-9=0, or 2x^2-12x+9=0<BR>\n" );
document.write( "x= (1/4)(12+/-sqrt(144-72)) or (1/4)(12+/-6 sqrt(2))<BR>\n" );
document.write( "roots are 3 +/- (3/2) sqrt(2)<BR>\n" );
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