document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=877615>Question 877615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find an equation of the parabola which passes through the points (1,3) and (-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 #529444 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=529444\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two points do not define a parabola.  Are you hoping for any parabola which will fit?  Infinite parabolas may hold any two given points.  One of your given points shows a \"root\", so you could begin by saying, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B2%29%28x-r%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B2%29%28x-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You have one more given point which you can use by saying, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=%281%2B2%29%281-r%29 ALIGN=MIDDLE  ALT=\"3=%281%2B2%29%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, assuming the leading coefficient on x^2 is 1.  \r<BR>\n" );
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document.write( "Now, with the coordinate values substituted, solve for r.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281-r%29=3 ALIGN=MIDDLE  ALT=\"3%281-r%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-3r=3 ALIGN=MIDDLE  ALT=\"3-3r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3r=0 ALIGN=MIDDLE  ALT=\"-3r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0 ALIGN=MIDDLE  ALT=\"r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Your possible parabola as an equation can be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%28x%2B2%29x%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%28x%2B2%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You can have any nonzero value for a for the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%28x%2B2%29 ALIGN=MIDDLE  ALT=\"y=ax%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this will also work with the two given points. </SPAN>\n" );
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