document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919274>Question 919274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am given three points on a graph (0, 1.8) (2,4) and (4,3) and am asked to find the equation of the parabola that these points pass through. I know that this parabola will be a maximum, and the y-intercept is at 1.8. <BR>\n" );
document.write( "I have tried putting the equations into each other by plugging in each point to their own equation, and then solving from that. I must have gone wrong somewhere because I ended up with y= 0.23x^2 - 0.64x + 1.8. I don't know how to move on, could you please help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557613 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=557613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rethink the points which are given.  A vertex maximum should occur between x=0 and x=4, and thinking visually or plotting on paper, you should understand and expect because of this maximum vertex, coefficient on x^2 will be a negative value.\r<BR>\n" );
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document.write( "Not seeing any more convenient method, form a system of three equations using the points.\r<BR>\n" );
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document.write( "y=ax^2+bx+c\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%2A0%5E2%2Bb%2A0%2Bc=1.8%2Ca%2A2%5E2%2Bb%2A2%2Bc=4%2Ca%2A4%5E2%2Bb%2A4%2Bc=3%29 ALIGN=MIDDLE  ALT=\"system%28a%2A0%5E2%2Bb%2A0%2Bc=1.8%2Ca%2A2%5E2%2Bb%2A2%2Bc=4%2Ca%2A4%5E2%2Bb%2A4%2Bc=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=system%280%2Aa%2B0b%2Bc=1.8%2C4a%2B2b%2Bc=4%2C16a%2B4b%2Bc=3%29 ALIGN=MIDDLE  ALT=\"system%280%2Aa%2B0b%2Bc=1.8%2C4a%2B2b%2Bc=4%2C16a%2B4b%2Bc=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Just substitute for c and obtain a system of two equations in a and b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%284a%2B2b%2B1.8=4%2C16a%2B4b%2B1.8=3%29 ALIGN=MIDDLE  ALT=\"system%284a%2B2b%2B1.8=4%2C16a%2B4b%2B1.8=3%29\"   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=system%284a%2B2b=2.2%2C16a%2B4b=1.2%29 ALIGN=MIDDLE  ALT=\"system%284a%2B2b=2.2%2C16a%2B4b=1.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Preparing for start of Elimination Method,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288a%2B4b=4.4%2C16a%2B4b=1.2%29 ALIGN=MIDDLE  ALT=\"system%288a%2B4b=4.4%2C16a%2B4b=1.2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "SUBTRACT the first equation from the second equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a%2B0b-3.2 ALIGN=MIDDLE  ALT=\"8a%2B0b-3.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8a=-3.2 ALIGN=MIDDLE  ALT=\"8a=-3.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-3.2%2F8 ALIGN=MIDDLE  ALT=\"a=-3.2%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and multiply by 5, just to simplify into a rational number.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-16%2F40 ALIGN=MIDDLE  ALT=\"a=-16%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-4%2F10 ALIGN=MIDDLE  ALT=\"a=-4%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=-2%2F5%29 ALIGN=MIDDLE  ALT=\"highlight%28a=-2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and already was found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=1.8%29 ALIGN=MIDDLE  ALT=\"highlight%28c=1.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Pick either equation from the two-equation, two variable system to solve for b.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2B2b=2.2 ALIGN=MIDDLE  ALT=\"4a%2B2b=2.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=2.2-4a ALIGN=MIDDLE  ALT=\"2b=2.2-4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1.1-2a ALIGN=MIDDLE  ALT=\"b=1.1-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1.1-2%28-2%2F5%29 ALIGN=MIDDLE  ALT=\"b=1.1-2%28-2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1.1%2B4%2F5 ALIGN=MIDDLE  ALT=\"b=1.1%2B4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1.1%2B0.8 ALIGN=MIDDLE  ALT=\"b=1.1%2B0.8\"   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=1.9%29 ALIGN=MIDDLE  ALT=\"highlight%28b=1.9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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