document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214367>Question 214367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can anyone help me with this problem? Find b and c so that the parabola y = -14 x^2 + b x + c has vertex (6 , 0 ).  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161911 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=161911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The vertex of a parabola is at x = -b/2a<BR>\n" );
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document.write( "your equation is:<BR>\n" );
document.write( "-14x^2 + bx + c = y<BR>\n" );
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document.write( "This equation is in standard form when y = 0.<BR>\n" );
document.write( "We get:<BR>\n" );
document.write( "-14x^2 + bx + c = 0<BR>\n" );
document.write( "a = -14<BR>\n" );
document.write( "b and c are unknown.<BR>\n" );
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document.write( "Equation for the vertex is x = -b/2a<BR>\n" );
document.write( "We know that we want the vertex at (6,0), so we are at the vertex when:<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "y = 0<BR>\n" );
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document.write( "substituting x = 6 in the equation for the vertex, we get:<BR>\n" );
document.write( "6 = -b/2a<BR>\n" );
document.write( "We know that a = -14, so this equation becomes:<BR>\n" );
document.write( "6 = -b/(-28)<BR>\n" );
document.write( "We solve for b to get:<BR>\n" );
document.write( "b = 168<BR>\n" );
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document.write( "Our equation now becomes:<BR>\n" );
document.write( "-14x^2 + 168x + c = y<BR>\n" );
document.write( "We know that the vertex is at (6,0) so we know that we want this equation to equal to 0 at the point x = 6.<BR>\n" );
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document.write( "We set y = 0 and we substitute 6 for x in the equation to get:<BR>\n" );
document.write( "-14*(6^2) + 168(6) + c = 0<BR>\n" );
document.write( "This becomes:<BR>\n" );
document.write( "-504 + 1008 + c = 0<BR>\n" );
document.write( "Thie becomes:<BR>\n" );
document.write( "504 + c = 0<BR>\n" );
document.write( "we solve for c to get:<BR>\n" );
document.write( "c = -504<BR>\n" );
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document.write( "Our equation becomes:<BR>\n" );
document.write( "y = -14x^2 + 168x - 504<BR>\n" );
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document.write( "Answer to your question is:<BR>\n" );
document.write( "b = 168<BR>\n" );
document.write( "c = -504<BR>\n" );
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document.write( "Graph of this equation is shown below:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-20%2C20%2C-1000%2C1000%2C-14x%5E2%2B168x-504%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-20%2C20%2C-1000%2C1000%2C-14x%5E2%2B168x-504%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Because a is negative, this graph opens downward.<BR>\n" );
document.write( "If a was positive, it would open upward.<BR>\n" );
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