document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=704340>Question 704340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me understand this question? I would like to know the process of how you come to the answers as I have a test tomorrow!<BR>\n" );
document.write( "y=-2(x-3)^2+8<BR>\n" );
document.write( "a)State the coordinates of the vertex<BR>\n" );
document.write( "b)State whether is has a max or min value and what that is?<BR>\n" );
document.write( "c)State the equation of the axis of symmetry<BR>\n" );
document.write( "d)State the y-intercept.<BR>\n" );
document.write( "If you could show me how you reach each answer..that would be amazing!<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434055 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=-2(x-3)^2+8<BR>\n" );
document.write( "a)State the coordinates of the vertex<BR>\n" );
document.write( "You have to remember the \"vertex form\" of a quadratic:<BR>\n" );
document.write( "y = a(x-h)^2 + k<BR>\n" );
document.write( "where (h,k) is the vertex<BR>\n" );
document.write( "since your equation was:<BR>\n" );
document.write( "y=-2(x-3)^2+8<BR>\n" );
document.write( "we immediately can see that the vertex is at:<BR>\n" );
document.write( "(h,k) = (3,8)<BR>\n" );
document.write( "b)State whether is has a max or min value and what that is?<BR>\n" );
document.write( "We can tell by the \"coefficient\" associated with the x^2 term:<BR>\n" );
document.write( "y=-2(x-3)^2+8<BR>\n" );
document.write( "expanding the above:<BR>\n" );
document.write( "y=-2(x^2-6x+9)+8<BR>\n" );
document.write( "y=-2x^2+12x-18+8<BR>\n" );
document.write( "y=-2x^2+12x-10<BR>\n" );
document.write( "Since it will be \"negative\" -- we conclude that it will be a parabola that opens downwards.  Thus the vertex will be the MAX.<BR>\n" );
document.write( "Note: do part c first, then come back to this<BR>\n" );
document.write( "c)State the equation of the axis of symmetry<BR>\n" );
document.write( "axis of symmetry is at:<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -12/(2(-2))<BR>\n" );
document.write( "x = -12/(-4)<BR>\n" );
document.write( "x = 3 (axis of symmetry)<BR>\n" );
document.write( "d)State the y-intercept.<BR>\n" );
document.write( "set x to zero:<BR>\n" );
document.write( "y=-2x^2+12x-10<BR>\n" );
document.write( "y=-2(0)^2+12(0)-10<BR>\n" );
document.write( "y=0+0-10<BR>\n" );
document.write( "y = -10<BR>\n" );
document.write( "y-intercept is at (0, -10)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );