document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320390>Question 320390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find where two parabolas y= -2(x-3)^2 + 4 and y=2(x-2)^2 -1 intersect each other.\r<BR>\n" );
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document.write( "I keep coming up with another quadratic equation instead of a point! I also tried sketching both parabolas, but the exact point of intersection is difficult to verify. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229442 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=229442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're getting a quadratic equation because they intersect at two points. <BR>\n" );
document.write( "If they only intersected at one point, you would get a linear equation.<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-2%2C10%2C+-10%2C+10%2C+-2%28x-3%29%5E2+%2B+4%2C+2%28x-2%29%5E2+-1%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x-3%29%5E2%2B4=2%28x-2%29%5E2+-1 ALIGN=MIDDLE  ALT=\"-2%28x-3%29%5E2%2B4=2%28x-2%29%5E2+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x%5E2-6x%2B9%29%2B4=2%28x%5E2-4x%2B4%29-1 ALIGN=MIDDLE  ALT=\"-2%28x%5E2-6x%2B9%29%2B4=2%28x%5E2-4x%2B4%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B12x-18%2B4=2x%5E2-8x%2B8-1 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B12x-18%2B4=2x%5E2-8x%2B8-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-20x%2B21=0 ALIGN=MIDDLE  ALT=\"4x%5E2-20x%2B21=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-7%29%282x-3%29=0 ALIGN=MIDDLE  ALT=\"%282x-7%29%282x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-7=0 ALIGN=MIDDLE  ALT=\"2x-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=7 ALIGN=MIDDLE  ALT=\"2x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7%2F2 ALIGN=MIDDLE  ALT=\"x=7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then use either equation to find y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%287%2F2-4%2F2%29%5E2-1 ALIGN=MIDDLE  ALT=\"y=2%287%2F2-4%2F2%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%283%2F2%29%5E2-1 ALIGN=MIDDLE  ALT=\"y=2%283%2F2%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9%2F2-2%2F2 ALIGN=MIDDLE  ALT=\"y=9%2F2-2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=7%2F2 ALIGN=MIDDLE  ALT=\"y=7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3=0 ALIGN=MIDDLE  ALT=\"2x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=3 ALIGN=MIDDLE  ALT=\"2x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Again, find y,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%283%2F2-4%2F2%29%5E2-1 ALIGN=MIDDLE  ALT=\"y=2%283%2F2-4%2F2%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%28-1%2F2%29%5E2-1 ALIGN=MIDDLE  ALT=\"y=2%28-1%2F2%29%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2F2-2%2F2 ALIGN=MIDDLE  ALT=\"y=-1%2F2-2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1%2F2 ALIGN=MIDDLE  ALT=\"y=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+300%2C+300%2C+-2%2C5%2C+-2%2C+5%2C+grid%281%29%2C%0D%0Acircle%283%2F2%2C-1%2F2%2C0.15%29%2C%0D%0Acircle%287%2F2%2C7%2F2%2C0.15%29%2C%0D%0Agraph%28+300%2C+300%2C+-2%2C5%2C+-2%2C+5%2C+-2%28x-3%29%5E2+%2B+4%2C+2%28x-2%29%5E2+-1%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "(7/2,7/2) and (3/2,-1/2)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );