document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=669596>Question 669596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem of algebra 2:\r<BR>\n" );
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document.write( "The general form of an equation for a parabola is y=ax^2+bx+c, where (x,y) is a point on the parabola. If three points on a parabola were (2,-10)(-5,-101)and (6,-90) determine the values of a, b and c write the general form of the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #416569 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=416569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form of an equation for a parabola is y=ax^2+bx+c, where (x,y) is a point on the parabola.<BR>\n" );
document.write( " If three points on a parabola were (2,-10)(-5,-101)and (6,-90) determine the<BR>\n" );
document.write( " values of a, b and c write the general form of the equation.<BR>\n" );
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document.write( "Use elimination or substitution to find a, b, c, write an equation for each pair<BR>\n" );
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document.write( "2,-10<BR>\n" );
document.write( "(2^2)a + 2b + c = -10<BR>\n" );
document.write( "4a + 2b + c = -10<BR>\n" );
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document.write( "-5,-101<BR>\n" );
document.write( "25a - 5b + c = -101<BR>\n" );
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document.write( "6,-90<BR>\n" );
document.write( "36a + 6b + c = -90<BR>\n" );
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document.write( "Eliminate c,<BR>\n" );
document.write( "subtract the 1st equation from the 2nd equation<BR>\n" );
document.write( "25a - 5b + c = -101<BR>\n" );
document.write( " 4a + 2b + c = -10<BR>\n" );
document.write( "-------------------Subtracting eliminates c<BR>\n" );
document.write( "21a - 7b = -91<BR>\n" );
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document.write( "subtract the 1st eq from the 3rd eq<BR>\n" );
document.write( "36a + 6b + c = -90<BR>\n" );
document.write( " 4a + 2b + c = -10<BR>\n" );
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document.write( "32a + 4b = -80<BR>\n" );
document.write( "4b = -32a - 80<BR>\n" );
document.write( "simplify divide by 4<BR>\n" );
document.write( "b = -8a - 20<BR>\n" );
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document.write( "Replace b with (-8a-20) in eq: 21a - 7b = -91<BR>\n" );
document.write( "21a - 7(-8a-20) = -91<BR>\n" );
document.write( "21a + 56a + 140 = -91<BR>\n" );
document.write( "77a = -91 - 140<BR>\n" );
document.write( "77a = -231<BR>\n" );
document.write( "a = -3<BR>\n" );
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document.write( "Find b, replace a<BR>\n" );
document.write( "b = -8(-3) - 20<BR>\n" );
document.write( "b = +24 - 20<BR>\n" );
document.write( "b = 4<BR>\n" );
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document.write( "Find c using the 1st equation<BR>\n" );
document.write( "4(-3) + 2(4) + c = -10<BR>\n" );
document.write( "-12 + 8 + c = -10<BR>\n" );
document.write( "-4 + c = -10<BR>\n" );
document.write( "c = -10 + 4<BR>\n" );
document.write( "c = -6<BR>\n" );
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document.write( "The equation:<BR>\n" );
document.write( "y = -3x^2 + 4x - 6<BR>\n" );
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document.write( "I checked this on my Ti83, to ensure the given pairs are on the graph<BR>\n" );
document.write( "you should do the same\r<BR>\n" );
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document.write( " </SPAN>\n" );
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