document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887363>Question 887363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a parabola, in standard form, that goes through these points:		<BR>\n" );
document.write( "(0, 3)      (1, 4)     (-1, -6)\r<BR>\n" );
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document.write( "Graph the parabola above.  Indicate the vertex and axis of symmetry. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536577 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=536577\">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=ax%5E2%2Bbx%2Bc=y ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=y\"   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=a%2A1%2Bb%2A1%2Bc=4 ALIGN=MIDDLE  ALT=\"a%2A1%2Bb%2A1%2Bc=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28-1%29%5E2%2Bb%28-1%29%2Bc=-6 ALIGN=MIDDLE  ALT=\"a%28-1%29%5E2%2Bb%28-1%29%2Bc=-6\"   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=0%2B0%2Bc=3 ALIGN=MIDDLE  ALT=\"0%2B0%2Bc=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc=4 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2Bc=-6 ALIGN=MIDDLE  ALT=\"a-b%2Bc=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The variables in this now  become a, b, c.<BR>\n" );
document.write( "The y-intercept point and its equation allow eliminating c so you can form two equations in just the unknowns a and b.\r<BR>\n" );
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document.write( "You already see <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=3%29 ALIGN=MIDDLE  ALT=\"highlight%28c=3%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=a%2Bb=4-c=4-3 ALIGN=MIDDLE  ALT=\"a%2Bb=4-c=4-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a%2Bb=1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a%2Bb=1%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=a-b=-6-c=-6-3 ALIGN=MIDDLE  ALT=\"a-b=-6-c=-6-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a-b=-9%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a-b=-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Add those two and you can solve for a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-5%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Use either of the a & b equations to find b.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1-a ALIGN=MIDDLE  ALT=\"b=1-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1-%28-5%29 ALIGN=MIDDLE  ALT=\"b=1-%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=6%29 ALIGN=MIDDLE  ALT=\"highlight%28b=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "General equation now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-5x%5E2%2B6x%2B3%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-5x%5E2%2B6x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Is that factorable?<BR>\n" );
document.write( "Discriminant, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A6-4%2A%28-5%29%2A3=36%2B60=96 ALIGN=MIDDLE  ALT=\"6%2A6-4%2A%28-5%29%2A3=36%2B60=96\"   DISABLED_style= \"max-width:90%; height:auto;\" >, quadratic is NOT factorable.\r<BR>\n" );
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document.write( "You still want the vertex maximum point in order to be able to graph y.<BR>\n" );
document.write( "You have your choice of completing the square to convert into standard form; or you can use the general solution of a quadratic equation to find the zeros and the vertex will be in the exact middle of the two solutions.\r<BR>\n" );
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document.write( "This may help:  <a  rel=nofollow HREF=\"http://www.algebra.com/tutors/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev\">Completing the Square to Solve General Quadratic Equation</a> </SPAN>\n" );
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