document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181909>Question 1181909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the factored form equation for a parabola that has x-intercepts at -3 and 1 and vertex point at (- 1, -8).  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811861 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=811861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "If p and q are roots of a quadratic, then x-p and x-q are the two factors.\r<BR>\n" );
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document.write( "Based on that, we have the roots -3 and 1 lead us to the factors (x+3) and (x-1)\r<BR>\n" );
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document.write( "Notice that the expression (x+3)(x-1), when set equal to zero, will result in x = -3 or x = 1 as the two roots. I'm using the zero product property.\r<BR>\n" );
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document.write( "In other words, solving (x+3)(x-1) = 0 will get us x = -3 and x = 1 as the two roots.\r<BR>\n" );
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document.write( "That takes care of the x intercept portion. Now let's consider the vertex point. \r<BR>\n" );
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document.write( "Let's see if plugging x = -1 leads to y = -8<BR>\n" );
document.write( "(x+3)(x-1) = (-1+3)(-1-1) = (2)(-2) = -4<BR>\n" );
document.write( "Unfortunately, we don't reach the target we want. <BR>\n" );
document.write( "We can fix this by sticking a 2 out front, so that we scale the -4 up to -8\r<BR>\n" );
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document.write( "Trying x = -1 again gets us<BR>\n" );
document.write( "2(x+3)(x-1) = 2(-1+3)(-1-1) = 2(2)(-2) = -8<BR>\n" );
document.write( "and now everything works out\r<BR>\n" );
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document.write( "Answer: <font color=red>2(x+3)(x-1)</font>\r<BR>\n" );
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document.write( "Graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"30%\" src = \"https://i.imgur.com/DJFsaXj.png\"><BR>\n" );
document.write( "Points A and B are the roots, aka x intercepts.<BR>\n" );
document.write( "Point C is the vertex. <BR>\n" );
document.write( "Because the vertex is below the x axis, and there are two x intercepts, this must mean the parabola opens upward (hence the positive leading coefficient a = 2)<BR>\n" );
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