document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147060>Question 147060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the quadradic function, whose graph is given?<BR>\n" );
document.write( "vertex (-2,2)<BR>\n" );
document.write( "y-intercept (0,-6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107408 by </B><A HREF=/tutors/aboutme.mpl?userid=giveback><B>giveback(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=giveback><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=107408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Quadratic function has the generic form as: y=ax^2+bx+c<BR>\n" );
document.write( "Our purpose is to find a, b and c.<BR>\n" );
document.write( "With information given as:<BR>\n" );
document.write( "  y-intercept is (0,-6) then we have: -6=a(0)^2+b(0)+c<BR>\n" );
document.write( "  from there we have c=-6 (we found c)<BR>\n" );
document.write( "  vertex is (-2,2) then we have 2=a(-2)^2+b(-2)-6 or 2a-b=4 <BR>\n" );
document.write( "  with vertex at (-2,2) we aslo have the line of symmetry as x=-2<BR>\n" );
document.write( "  meaning as x=-4, y=-6 then -6=a(-4)^2+b(-4)-6 or 4a-b=0 or b=4a<BR>\n" );
document.write( "  substitute b=4a into the equation 2a-b=4 we have 2a-4a=4 or a=-2 (we found a)<BR>\n" );
document.write( "  substitute a=-2 into the equation b=4a we find b=-8 (we found b)<BR>\n" );
document.write( "Then our quadratic function is: y=-2x^2-8x-6    <BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );