document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132482>Question 1132482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic equation whose root are -1/4 and 3.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749530 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=749530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the roots are at x = -1/4 and x = 3.<BR>\n" );
document.write( "set these equations to 0 by doing the following.<BR>\n" );
document.write( "add 1/4 to both sides of x = -1/4 to get x + 1/4 = 0<BR>\n" );
document.write( "subtract 3 from both sides of x = 3 to get x - 3 = 0<BR>\n" );
document.write( "the factors of the quadratic equation are (x + 1/4) * (x - 3) = 0<BR>\n" );
document.write( "set the equation equal to y and simplify to get:<BR>\n" );
document.write( "y = x^2 - 3x + 1/4 * x - 3/4<BR>\n" );
document.write( "combine like terms to get y = x^2 - 2.75x - 3/4<BR>\n" );
document.write( "in fact, the quadratic equation can be a * (x^2 - 2.75x - 3/4)<BR>\n" );
document.write( "if a = 1, you get x^2 - 2.75x - 3/4.<BR>\n" );
document.write( "if a = 4, you get 4x^2 - 11x - 3.<BR>\n" );
document.write( "a can be any value and the roots of the equation will be the same.<BR>\n" );
document.write( "the graph above shows the basic equation of x^2 - 2.75x - 3/4 with various values of a to show that the roots remain the same even though the quadratic equation itself is different after being gernerated by the diffedrent values of a.<BR>\n" );
document.write( "the two versions of the red equation show you that they are, in fact, the same equivalent equations that generate the same red graph.<BR>\n" );
document.write( "here's the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/010902.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's some references.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://mathbitsnotebook.com/Algebra1/Quadratics/QDGetEquation.html\" target= \"_blank\">https://mathbitsnotebook.com/Algebra1/Quadratics/QDGetEquation.html</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/fromzero.htm\" target= \"_blank\">https://www.purplemath.com/modules/fromzero.htm</a>\r<BR>\n" );
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