document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828362>Question 828362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, <BR>\n" );
document.write( "So I missed my Pre-Ap Algebra II class, and I was wondering how I would be able to find a quadratic function that includes each set of Values. <BR>\n" );
document.write( "So, the question that I was working on gave me three points, which are (1,-2),(2,-2), and (3,-4). <BR>\n" );
document.write( "I did look in the textbook, and I attempted to try each. This is what I have so far. <BR>\n" );
document.write( "*y=ax^2+bx=c<BR>\n" );
document.write( "-2=A(-1)^2+b(1)+c<BR>\n" );
document.write( "-2=a+b+c<BR>\n" );
document.write( "*y=ax^2+bx=c<BR>\n" );
document.write( "-2=a(2)^2+b(2)+c <BR>\n" );
document.write( "-2=4a+2b+c<BR>\n" );
document.write( "*y=ax^2+bx=c<BR>\n" );
document.write( "-4=a(3)^2=b(3)=c<BR>\n" );
document.write( "-4=9a+3b+c<BR>\n" );
document.write( "So thats what I have so far, but in the example i noticed it said \"use one of the methods in chap.3\" and solve. Im not sure what to do after all of that from above. I just want to know which way is the easiest and will help me with my following homework problems. I was also wondering if there was any way to check it to make sure my answer will be right with this and the upcoming problems that I have to solve. <BR>\n" );
document.write( "Thank you so much for your time and help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499315 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=499315\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Some of your steps are not clear.  You could use the given three points to form three equations with unknown coefficients and use very simple linear algebra skills to find the values of these coefficients.  \r<BR>\n" );
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document.write( "You can also use the quality of symmetry for a quadratic equation of a parabola, and find the x value of the center, so you know the vertex is on that line of symmetry.  Having points (1,-2) and (2,-2), you know that because of symmetry, this parabola has a vertex on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Looking at the other given point on the parabola, (3,-4), you understand that the \"a\" coefficient on x^2 is negative; the value of the function decreases as x moves away from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the function has a MAXIMUM at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "LOOK AT the standard form equation for your so-far-unfinished function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-3%2F2%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-3%2F2%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Plug in the point (3,-4).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=a%283-3%2F2%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"-4=a%283-3%2F2%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=a%289%2F4%29%2Bk ALIGN=MIDDLE  ALT=\"-4=a%289%2F4%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16=9a%2B4k ALIGN=MIDDLE  ALT=\"-16=9a%2B4k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%2B4k=-16 ALIGN=MIDDLE  ALT=\"9a%2B4k=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----nice linear equation.<BR>\n" );
document.write( "NOW, use that same standard form equation and substitute for either (1,-2) OR (2,-2).  No matter which; just choose either.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=a%282-3%2F2%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"-2=a%282-3%2F2%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=a%281%2F4%29%2Bk ALIGN=MIDDLE  ALT=\"-2=a%281%2F4%29%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8=a%2B4k ALIGN=MIDDLE  ALT=\"-8=a%2B4k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B4k=-8 ALIGN=MIDDLE  ALT=\"a%2B4k=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >----another very nice linear equation.<BR>\n" );
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document.write( "Solve this system of two linear equations in the unknowns, a and k.<BR>\n" );
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document.write( "9a+4k=-16<BR>\n" );
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document.write( "a+4k=-8<BR>\n" );
document.write( "------------------------\r<BR>\n" );
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document.write( "Once solved for a and k, finish your standard form equation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-3%2F2%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-3%2F2%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------------------------<BR>\n" );
document.write( "note:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and therefore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-7%2F4 ALIGN=MIDDLE  ALT=\"k=-7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, easily found through Elimination Method.  Finished standard form parabola, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%28x-3%2F2%29%5E2-7%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%28x-3%2F2%29%5E2-7%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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