document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=401463>Question 401463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I graph points (i.e (0,0), (3,-2), (4,-5)) on a coordinate plane? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285062 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=285062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do I graph points (i.e (0,0), (3,-2), (4,-5)) on a coordinate plane?\r<BR>\n" );
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document.write( "Remember the form of a quadratic equation:<BR>\n" );
document.write( "y=ax^2+bx+c<BR>\n" );
document.write( "We do not know whether this is a quadratic equation, but we can try to find a, b, and c, then graph it to find out if it is a quadratic equation.\r<BR>\n" );
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document.write( "for coordinates(0,0), 0=a(0^2)+b*0+c<BR>\n" );
document.write( "0=c<BR>\n" );
document.write( "c=0<BR>\n" );
document.write( "for coordinates(3,-2), -2=a(3^2)+3b+c<BR>\n" );
document.write( "-2=9a+3b+c<BR>\n" );
document.write( "9a+3b+c=-2<BR>\n" );
document.write( "for coordinates(4,-5), -5=a(4^2)+4b+c<BR>\n" );
document.write( "-5=a(16)+4b+c<BR>\n" );
document.write( "16a+4b+c=-5\r<BR>\n" );
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document.write( "we now have 3 equations with 3 unknowns, but c=0, so we only have two of the unknowns, a and b, to solve\r<BR>\n" );
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document.write( "9a+3b=-2<BR>\n" );
document.write( "16a+4b=-5<BR>\n" );
document.write( "multiply first equation by 4, and second equation by -3<BR>\n" );
document.write( "36a+12b=-8<BR>\n" );
document.write( "-48a-12b=+15<BR>\n" );
document.write( "-12a=7<BR>\n" );
document.write( "a=-7/12<BR>\n" );
document.write( "b=(-2-9a)/3<BR>\n" );
document.write( " =((-8/4-(9*-7/12))/3<BR>\n" );
document.write( " =(-8/4+21/4)/3<BR>\n" );
document.write( " =(13/4)/3<BR>\n" );
document.write( "b=13/12<BR>\n" );
document.write( "we now have an equation which appears to  be a parabola.<BR>\n" );
document.write( "f(x)=-(7/12)x^2+(13/12)x+0\r<BR>\n" );
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document.write( "see the graph below: note the 3 given coordinates,(0,0),(3,-2),and (4,-5) on the curve \r<BR>\n" );
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document.write( " </SPAN>\n" );
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