document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764034>Question 764034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quadratic equation has a parable that has the roots x = 3 and x = -5. It passes through the point (1, -12). Determine its equation <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 #465172 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=465172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A quadratic equation has a parabola that has the roots x = 3 and x = -5.<BR>\n" );
document.write( " It passes through the point (1, -12).<BR>\n" );
document.write( " Determine it's equation.<BR>\n" );
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document.write( "Using the form ax^2 + bx + c = y, write equation for each pair<BR>\n" );
document.write( "x=3; y = 0: 9a + 3b + c = 0<BR>\n" );
document.write( "x=-.5; y=0: .25a - .5b + c = 0<BR>\n" );
document.write( "x=1; y=-12: a + b + c = -12<BR>\n" );
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document.write( "Subtract the 3rd equation from the 1st equation<BR>\n" );
document.write( "9a + 3b + c = 0<BR>\n" );
document.write( " a + b + c = -12<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "8a + 2b = 12<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "4a + b = 6<BR>\n" );
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document.write( "Subtract the 3rd equation from the 2nd equation<BR>\n" );
document.write( ".25a - .5b + c = 0<BR>\n" );
document.write( " a + b + c = -12<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "-.75a - 1.5b = 12<BR>\n" );
document.write( "Simplify, divide both sides by -.75<BR>\n" );
document.write( "a + 2b = -16<BR>\n" );
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document.write( "Two 2 unknown equations we can solve with elimination<BR>\n" );
document.write( "Multiply the 1st by 2, subtract the 2nd<BR>\n" );
document.write( "8a + 2b = 12<BR>\n" );
document.write( " a + 2b = -16<BR>\n" );
document.write( "-----------------subtraction eliminates b, find a<BR>\n" );
document.write( "7a = 28<BR>\n" );
document.write( "a = 28/7<BR>\n" );
document.write( "a = 4<BR>\n" );
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document.write( "Find b using a + 2b = -16<BR>\n" );
document.write( "4 + 2b = -16<BR>\n" );
document.write( "2b = -20<BR>\n" );
document.write( "b = -10<BR>\n" );
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document.write( "Find c<BR>\n" );
document.write( "4 - 10 + c = -12<BR>\n" );
document.write( "c = -12 + 6<BR>\n" );
document.write( "c = -6<BR>\n" );
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document.write( "Our equation: y = 4x^2 - 10x - 6<BR>\n" );
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document.write( "Graphically<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-5%2C+5%2C+-20%2C+10%2C+4x%5E2-10x-+6%29 ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-5%2C+5%2C+-20%2C+10%2C+4x%5E2-10x-+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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