document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27358>Question 27358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We have had extreme trouble with this one. There are four of us and each of us comes up with a different polynomial to the fourth degree. Here it is: We have a circle (x-1)^2 + y^2 = 8 intersected by the parabola y = 1/4(x-1)^2 + 1. The question wants us to find the points of intersection between the parabola and the circle. We can see by the graph that the parabola intersects the circle at (-1,2) and (3,2) but we are having trouble with the actual equation. We know that we need to substitute and get this equation: (x-1)^2 + [1/4(x-1)^2 + 1]^2 = 8. This is where we are having troubles with simplifying the polynomial - we all get a different polynomial to the fourth degree. Can someone help? We would really appreciate a step-by-step to see where we are going wrong.\r<BR>\n" );
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document.write( "Thanks for your help<BR>\n" );
document.write( "Melissa </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14884 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=14884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the parabola equation for (x-1)^2 as follows:<BR>\n" );
document.write( "Multiply through be \"4\" to get:<BR>\n" );
document.write( "4y-4=(x-1)^2<BR>\n" );
document.write( "Substitute that into the circle equation to get:<BR>\n" );
document.write( "4y-4+y^2=8<BR>\n" );
document.write( "y^2+4y-12=0<BR>\n" );
document.write( "(y+6)(y-2)=0<BR>\n" );
document.write( "y=-6 or y=2<BR>\n" );
document.write( "Plug those values into the original circle equation one<BR>\n" );
document.write( "at a time:<BR>\n" );
document.write( "If y=-6 then (x-1)^2+36=8<BR>\n" );
document.write( "Then (x-1)^2=-28<BR>\n" );
document.write( "This has no Real number solution so forget it.<BR>\n" );
document.write( "If y=2 then (x-1)^2+4=8<BR>\n" );
document.write( "(x-1)^2=4<BR>\n" );
document.write( "So, x-1=2 or x-1=-2<BR>\n" );
document.write( "x=3 or x=-1<BR>\n" );
document.write( "Solutions: (3,2) (-1,2)\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );