document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56581>Question 56581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Generate a graph for the following function g(x)=-4x^2 + 16x-19<BR>\n" );
document.write( "Find the vertex and x and y intercepts for the graph, show all work </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38486 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=38486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> g(x)=-4x^2 + 16x-19<BR>\n" );
document.write( "Find the vertex and x and y intercepts for the graph<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "y-intercept: Let x=0, then g(x)=-19; this is the y-intercept.<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "x-intercept: Let g(x)=0, then -4x^2+16x-19=0<BR>\n" );
document.write( "x=[-16+-sqrt(256-304)]/-8<BR>\n" );
document.write( "x=2+-(1/4)isqrt3]<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "To get the vertex:<BR>\n" );
document.write( "4x^2-16x+? = -y-19<BR>\n" );
document.write( "x^2-4x+? =(-1/4)y-(19/4)<BR>\n" );
document.write( "Complete the square to get:<BR>\n" );
document.write( "x^2-4x+4=(-1/4)y-19/4 +16/4<BR>\n" );
document.write( "(x-2)^2 = (-1/4)y-(3/4)<BR>\n" );
document.write( "(x-2)^2 = (-1/4)(y+3)<BR>\n" );
document.write( "Vertex at (2,-3)<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );