document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468343>Question 468343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the value of c if the vertex of the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2-8x%2Bc ALIGN=MIDDLE  ALT=\"y=x%5E2-8x%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a point one x-axis? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321337 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the vertex is on the x_axis, then the y_value of vertex must be 0.<BR>\n" );
document.write( "Vertex: (x_value, 0)<BR>\n" );
document.write( "To determine x-value of vertex, use formula for finding line of symmetry<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the given parabola, a = 1, b = -8, c = c<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F2+=+4 ALIGN=MIDDLE  ALT=\"x+=+8%2F2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore the vertex is at (4,0)<BR>\n" );
document.write( "To solve for c, plug in these values for x,y into given equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+-8x+%2Bc ALIGN=MIDDLE  ALT=\"y+=+x%5E2+-8x+%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+4%5E2+-%288%29%284%29+%2B+c ALIGN=MIDDLE  ALT=\"0+=+4%5E2+-%288%29%284%29+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+16+-+32+%2B+c ALIGN=MIDDLE  ALT=\"0+=+16+-+32+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16+%2B+c ALIGN=MIDDLE  ALT=\"0+=+-16+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+c ALIGN=MIDDLE  ALT=\"16+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So value of c is 16.<BR>\n" );
document.write( "Any other value other than 16 would yield a vertex not on the x-axis.<BR>\n" );
document.write( " </SPAN>\n" );
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