document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066249>Question 1066249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the quadratic function f(x)=3x^2+6x+2<BR>\n" );
document.write( "a.)Graph the quadratic function by determining whether its graph opens up or down and by finding the vertex, axis of symmetry, y intercept, x intercepts, if any.<BR>\n" );
document.write( "b.)The domain of f is<BR>\n" );
document.write( "the range of f is<BR>\n" );
document.write( "c.)determine where the function is increasing and where it is decreasing. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681441 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=681441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=3x^2+6x+2<BR>\n" );
document.write( "function opens upward because positive coefficient in front of x^2.  It decreases from x=-oo to x=-1 and increases from x >-1.<BR>\n" );
document.write( "domain is all x. <BR>\n" );
document.write( "vertex x-value is -b/2a or -6/3(2)=-1<BR>\n" );
document.write( "f(-1)=3-6+2=-1. <BR>\n" );
document.write( "Vertex is (-1,-1)<BR>\n" );
document.write( "axis of symmetry is x=-1<BR>\n" );
document.write( "Range is [-1,oo)<BR>\n" );
document.write( "y intercept is at f(0), and that = 2<BR>\n" );
document.write( "x-intercepts need quadratic formula<BR>\n" );
document.write( "x=(1/6)(-6 +/- sqrt (36-24))= (1/6)(-6 +/- 2 sqrt (3))= -1 +/- ((1/3) sqrt (3)).  Numerically, they are -.42 and -1.58\r<BR>\n" );
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