document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180506>Question 1180506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Algebraically determine the point(s) of intersection between the following functions.<BR>\n" );
document.write( "f(x) = 2x^2+3<BR>\n" );
document.write( "g(x) = −3x+8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810204 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%E2%80%89=+2x%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29%E2%80%89=+2x%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+-3x%2B8 ALIGN=MIDDLE  ALT=\"g%28x%29+=+-3x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%E2%80%89=g%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29%E2%80%89=g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3=+-3x%2B8 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3=+-3x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3%2B3x-8=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3%2B3x-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B3x-5=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B3x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-5%29+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A2%2A%28-5%29+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+7%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+7%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B+7%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B+7%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+-+7%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+-+7%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F2 ALIGN=MIDDLE  ALT=\"x=-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of the intersection point\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%E2%80%89=+2%2A1%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29%E2%80%89=+2%2A1%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%E2%80%89=+5 ALIGN=MIDDLE  ALT=\"f%28x%29%E2%80%89=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "one  point of intersection between the following functions is: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%E2%80%89=+2%2A%28-5%2F2%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29%E2%80%89=+2%2A%28-5%2F2%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%E2%80%89=+31%2F2 ALIGN=MIDDLE  ALT=\"f%28x%29%E2%80%89=+31%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "second  point of intersection between the following functions is: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F2 ALIGN=MIDDLE  ALT=\"-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31%2F2 ALIGN=MIDDLE  ALT=\"31%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+20%2C+%0D%0Acircle%281%2C5%2C.13%29%2Clocate%281%2C5%2Cp%281%2C5%29%29%2C%0D%0Acircle%28-5%2F2%2C31%2F2%2C.13%29%2Clocate%28-5%2F2%2C31%2F2%2Cp%28-5%2F2%2C31%2F2%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+20%2C+2x%5E2%2B3%2C+-3x%2B8%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );