document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828351>Question 828351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the parabola that passes through the following points.<BR>\n" );
document.write( "(0,-12), (6,12), (2,-8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499258 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=499258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(0,-12)<BR>\n" );
document.write( "-12 = c<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(6,12)<BR>\n" );
document.write( "12 = a36 + b6 + c<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(2,-8)<BR>\n" );
document.write( "-8 = a4 + b2 + c<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the linear system:<BR>\n" );
document.write( "-12 = c<BR>\n" );
document.write( "12 = a36 + b6 + c<BR>\n" );
document.write( "-8 = a4 + b2 + c<BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = a<BR>\n" );
document.write( "y = b<BR>\n" );
document.write( "z = c<BR>\n" );
document.write( "---<BR>\n" );
document.write( "-12 = z<BR>\n" );
document.write( "12 = 36x + 6y + z<BR>\n" );
document.write( "-8 = 4x + 2y + z<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z = -12<BR>\n" );
document.write( "36x + 6y + z = 12<BR>\n" );
document.write( "4x + 2y + z = -8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above linear system in standard form into this matrix-method solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution:<BR>\n" );
document.write( "x = a = 0.5<BR>\n" );
document.write( "y = b = 1<BR>\n" );
document.write( "z = c = -12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "system matrix<BR>\n" );
document.write( "0 0 1<BR>\n" );
document.write( "36 6 1<BR>\n" );
document.write( "4 2 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "inverse of system matrix<BR>\n" );
document.write( "0.083333333 0.041666667 -0.125<BR>\n" );
document.write( "-0.66666667 -0.083333333 0.75<BR>\n" );
document.write( "1 0 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "determinant of system matrix = 48<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "y = 0.5x^2 + x - 12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );