document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572994>Question 572994</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation in standard form of the parabola passing through the following points.<BR>\n" );
document.write( "(0,-4),(1,1),(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 #368626 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=368626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find an equation in standard form of the parabola passing through the following points.<BR>\n" );
document.write( "(0,-4),(1,1),(2,8)<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Standard form of equation for a parabola: y=A(x-h)^2+k, (h,k) being the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Solve for A, h and k with the following 3 equations using 3 given points:<BR>\n" );
document.write( "1)-4=A(0-h)^2+k<BR>\n" );
document.write( "2)1=A(1-h)^2+k<BR>\n" );
document.write( "3)8=A(2-h)^2+k<BR>\n" );
document.write( "..<BR>\n" );
document.write( "1)-4=A(h)^2+k<BR>\n" );
document.write( "2)1=A(1-h)^2)+k<BR>\n" );
document.write( "subtract, to eliminate k<BR>\n" );
document.write( "3)-5=A(h^2-(1-h)^2)<BR>\n" );
document.write( "-5=A(h^2-1+2h-h^2)<BR>\n" );
document.write( "-5=A(-1+2h<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2)1=A(1-h)^2+k<BR>\n" );
document.write( "3)8=A(2-h)^2+k<BR>\n" );
document.write( "subtract to eliminate k<BR>\n" );
document.write( "4)-7=A(1-h)^2-(2-h)^2)<BR>\n" );
document.write( "-7=A(1-2h+h^2-4+4h-h^2)<BR>\n" );
document.write( "-7=A(-3+2h)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "-5=A(-1+2h<BR>\n" );
document.write( "-7=A(-3+2h)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "-5=-A+2hA<BR>\n" );
document.write( "-7=-3A+2hA<BR>\n" );
document.write( "subtract<BR>\n" );
document.write( "2=2A<BR>\n" );
document.write( "A=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "-5=-A+2hA<BR>\n" );
document.write( "-5=-1+2h<BR>\n" );
document.write( "2h=-4<BR>\n" );
document.write( "h=-2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "1=A(1-h)^2+k (eq 2)<BR>\n" );
document.write( "1=1*(1+2)^2+k<BR>\n" );
document.write( "1=9+k<BR>\n" );
document.write( "k=-8<BR>\n" );
document.write( "..<BR>\n" );
document.write( "A=1, h=-2, k=-8<BR>\n" );
document.write( "Equation of Parabola<BR>\n" );
document.write( "y=A(x-h)^2+k<BR>\n" );
document.write( "y=(x+2)^2-8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );