document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189357>Question 1189357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parabola having an axis parallel to the y-axis passes through points A(1,1) B(2,2) & C(-1,5). Find the equation <BR>\n" );
document.write( "of the parabola.<BR>\n" );
document.write( "a. x^2  -  2x  -  y + 2 = 0 <BR>\n" );
document.write( "b. y^2  -  2x  -  y + 2 = 0 <BR>\n" );
document.write( "c. y^2  -  x  -  2y + 2 = 0 <BR>\n" );
document.write( "d. x^2  -  x  -  2y + 2 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820708 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution from the other tutor is fine... but he went to a lot of trouble to find the equation of the parabola from his original three equations.<br><BR>\n" );
document.write( "y=ax^2+bx+c<br><BR>\n" );
document.write( "(1,1): a+b+c=1 [1]<BR>\n" );
document.write( "(2,2): 4a+2b+c=2 [2]<BR>\n" );
document.write( "(-1,5): a-b+c=5 [3]<br><BR>\n" );
document.write( "Observe that the coefficients of a and b in [1] and [3] are the same.  So subtracting one of those equations from the other will immediately give us b.<br><BR>\n" );
document.write( "2b=-4<BR>\n" );
document.write( "b=-2<br><BR>\n" );
document.write( "Now substitute b=-2 in [1] and [2]:<br><BR>\n" );
document.write( "a-2+c=1; a+c=3<BR>\n" );
document.write( "4a-4+c=2; 4a+c=6<BR>\n" );
document.write( "3a=3<BR>\n" );
document.write( "a=1<br><BR>\n" );
document.write( "Substitute a=1 and b=-2 in [1] to find c:<br><BR>\n" );
document.write( "1-2+c=1; c=2<br><BR>\n" );
document.write( "We have a=1, b=-2, c=2.<br><BR>\n" );
document.write( "ANSWER: y=x^2-2x+2 -- which is equivalent to answer choice a<br><BR>\n" );
document.write( "Of course, if this were a question on a multiple choice test, you would simply eliminate answer choices b and c because they contain y^2 terms instead of x^2 terms (making them equations of parabolas with axis parallel to the x-axis).  Then you would simply substitute the coordinates of the given points to determine which of answer choices a and d is correct.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );