document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=284270>Question 284270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi i need help with this problem for college algebra. <BR>\n" );
document.write( "write the equation of the parabola that has x-intercepts (-1,0) and (3,0) and y-intercept (0,6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #206304 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=206304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y-intercept of (0,6) means that y is equal to 6 when x is equal to 0.\r<BR>\n" );
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document.write( "The constant in the equation therefore needs to be 6.\r<BR>\n" );
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document.write( "general form of the equation is ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "with c = 6, general form becomes ax^2 + bx + 6 = 0\r<BR>\n" );
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document.write( "x-intercepts of (-1,0) and (3,0) are the roots of the equation.\r<BR>\n" );
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document.write( "this means that the roots are x = -1 and x = 3.\r<BR>\n" );
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document.write( "this means that x+1 = 0 and x-3 = 0.\r<BR>\n" );
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document.write( "this means that your equation is (x+1) * (x-3) = 0.\r<BR>\n" );
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document.write( "multiply those factors out and you get:\r<BR>\n" );
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document.write( "x^2 - 2x - 3 = 0\r<BR>\n" );
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document.write( "but c in the equation needed to be 6.\r<BR>\n" );
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document.write( "multiply both sides of your equation by -2 to get:\r<BR>\n" );
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document.write( "-2x^2 + 4x + 6 = 0\r<BR>\n" );
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document.write( "that should be your equation.\r<BR>\n" );
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document.write( "a graph of that equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-10%2C10%2C-2x%5E2+%2B+4x+%2B+6%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-10%2C10%2C-2x%5E2+%2B+4x+%2B+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The graph looks good.\r<BR>\n" );
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document.write( "The y-intercept is 6 as it should be.\r<BR>\n" );
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document.write( "The roots of the equation are -1 and 3 as they should be.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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