document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1114193>Question 1114193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic equation that fits the following set of data points.<BR>\n" );
document.write( "(&#8722;2&#8203;,&#8722;8&#8203;),(&#8722;4&#8203;,&#8722;12&#8203;),(1&#8203;,13&#8203;)<BR>\n" );
document.write( "&#8203;f(x)=______.<BR>\n" );
document.write( "&#8203;(Use integers or fractions for any numbers in the expression. Do not&#8203; factor.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #729201 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=729201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the standard form of your quadratic equation is:\r<BR>\n" );
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document.write( "y = ax^2 + bx + c\r<BR>\n" );
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document.write( "when x = -2 and y = -8, this equation becomes:\r<BR>\n" );
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document.write( "-8 = 4a -2b + c\r<BR>\n" );
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document.write( "when x = -4, this equation becomes:\r<BR>\n" );
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document.write( "-12 = 16a - 4b + c\r<BR>\n" );
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document.write( "when x = 1, this equation becomes:\r<BR>\n" );
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document.write( "13 = a + b + c\r<BR>\n" );
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document.write( "you have 3 equations thst need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "-8 = 4a - 2b + c<BR>\n" );
document.write( "-12 = 16a - 4b + c<BR>\n" );
document.write( "13 = a + b + c\r<BR>\n" );
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document.write( "you can reorder the terms to get:\r<BR>\n" );
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document.write( "4a - 2b + c = -8<BR>\n" );
document.write( "16a - 4b + c = -12<BR>\n" );
document.write( "a + b + c = 13\r<BR>\n" );
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document.write( "they are now in standard linear equation form.\r<BR>\n" );
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document.write( "when you solve these equations simultaneously, you will find that:\r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = 8<BR>\n" );
document.write( "c = 4\r<BR>\n" );
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document.write( "since the standard form of your equation is y = ax^2 + bx + c, you get:\r<BR>\n" );
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document.write( "y = x^2 + 8x + 4\r<BR>\n" );
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document.write( "that's your quadratic equation.\r<BR>\n" );
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document.write( "when x = -2, you get y = (-2)^2 - 8*2 + 4 = -8\r<BR>\n" );
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document.write( "when x = -4, you get y = (-4)^2 - 8*4 + 4 = -12\r<BR>\n" );
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document.write( "when x = 1, you get y = 1^2 - 8*1 + 4 = 13\r<BR>\n" );
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document.write( "this confirms your equation is correct.\r<BR>\n" );
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document.write( "i'm assuming you know how to solve 3 equations in 3 unknowns simultaneously.\r<BR>\n" );
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document.write( "i solved as follows.<BR>\n" );
document.write( "reference the worksheet shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/040802.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "i started with equations 1, 2, and 3.<BR>\n" );
document.write( "those are the circled numbers on the worksheet.\r<BR>\n" );
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document.write( "i then took equation 2 as is and multiplied equation 1 by 4 to get equation 4.\r<BR>\n" );
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document.write( "i then subtracted equation 4 from equation 2 to get equation 5.\r<BR>\n" );
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document.write( "i then took equation 2 as is and multiplied equation 3 by 16 to get equation 6.\r<BR>\n" );
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document.write( "i then subtracted equation 6 from equation 2 to get equation 7.\r<BR>\n" );
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document.write( "i then copied down equation 5 and 7 and proceeded to reduced these further so that i could solve for a single variable.\r<BR>\n" );
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document.write( "i multiplied equation 5 by 5 to get equation 8 and kept equation 7 as is.\r<BR>\n" );
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document.write( "i then subtracted equation 7 from equation 8 to get equation 9.\r<BR>\n" );
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document.write( "i then solved equation 9 for c to get c = 4\r<BR>\n" );
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document.write( "i then took equation 5 and replaced c with 4 and solved for b to get b = 8.\r<BR>\n" );
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document.write( "i then took equation 1 and replaced c with 4 and b with 8 and solved for a to get a = 1.\r<BR>\n" );
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document.write( "the result was a = 1, b = 8, c = 4.\r<BR>\n" );
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document.write( "that led to y = x^2 + 8x + 4, which is the solution shown above.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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