document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328470>Question 328470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic in standard form that goes through (-4,27), (1,2) (3,34)<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 #235269 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=235269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic in standard form that goes through (-4,27), (1,2) (3,34)<BR>\n" );
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document.write( "Using the form, ax^2 + bx + c = y, write an equation for each pair<BR>\n" );
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document.write( "x=-4, y=27<BR>\n" );
document.write( "a(-4^2) + b(-4) + c = 27<BR>\n" );
document.write( "16a - 4b + c = 27<BR>\n" );
document.write( "Do the same with the other two pairs<BR>\n" );
document.write( "x=1, y=2<BR>\n" );
document.write( "a + b + c = 1<BR>\n" );
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document.write( "x=3, y=34<BR>\n" );
document.write( "9a + 3b + c = 34<BR>\n" );
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document.write( "Subtract the 2nd equation from the 1st equation<BR>\n" );
document.write( "16a - 4b + c = 27<BR>\n" );
document.write( " a + b + c = 2<BR>\n" );
document.write( "--------------------eliminates c<BR>\n" );
document.write( "15a - 5b = 25<BR>\n" );
document.write( "simplify divide by 5<BR>\n" );
document.write( "3a - b = 5<BR>\n" );
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document.write( "Subtract the 2nd equation from the 3rd equation<BR>\n" );
document.write( "9a + 3b + c = 34<BR>\n" );
document.write( " a + b + c = 2<BR>\n" );
document.write( "--------------------Eliminates c<BR>\n" );
document.write( "8a + 2b = 32<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "4a + b = 16<BR>\n" );
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document.write( "Two equation which we can handle easily with elimination again<BR>\n" );
document.write( "3a - b = 5<BR>\n" );
document.write( "4a + b = 16<BR>\n" );
document.write( "---------------adding eliminates b, find a<BR>\n" );
document.write( "7a = 21<BR>\n" );
document.write( "a = 21/7<BR>\n" );
document.write( "a = 3<BR>\n" );
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document.write( "Find b using the equation 4a + b = 16, <BR>\n" );
document.write( "4(3) + b = 16<BR>\n" );
document.write( "12 + b = 16<BR>\n" );
document.write( "b = 16 - 12<BR>\n" );
document.write( "b = 4<BR>\n" );
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document.write( "Find c using the equation a + b + c = 2<BR>\n" );
document.write( "3 + 4 + c = 2<BR>\n" );
document.write( "c = 2 - 7<BR>\n" );
document.write( "c = -5<BR>\n" );
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document.write( "The equation: y = 3x^2 + 4x - 5<BR>\n" );
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document.write( "You can prove this to yourself by substituting for x and finding y for each pair </SPAN>\n" );
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