document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116801>Question 116801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> consider the function: f(x)= x^2+6x-2. Find h, the x-coordinate of the vertex of this parabola. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84912 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+x%5E2%2B6x-2 ALIGN=MIDDLE  ALT=\"f%28x%29=+x%5E2%2B6x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This function is of the standard form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Recall the quadratic formula that says for a function of this form the solutions for x are:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282%2Aa%29+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282%2Aa%29+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The first term on the right side (that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"-b%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will give you the value for x<BR>\n" );
document.write( "at the vertex of the parabolic graph for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"y+=+ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Comparing the given function with the standard form you can see that a in the standard form<BR>\n" );
document.write( "[the multiplier of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >] is +1 in the given problem, and b in the standard form<BR>\n" );
document.write( "[the multiplier of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >] is +6 in the given problem, and c (which we don't need) in <BR>\n" );
document.write( "the standard function is -2 in the given problem.<BR>\n" );
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document.write( "All you now have to do to solve this problem is plug the values for a and b into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"-b%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you get that the value of x at the vertex is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282%2Aa%29+=+-%28%2B6%29%2F%282%2A1%29+=+-6%2F2+=+-3 ALIGN=MIDDLE  ALT=\"-b%2F%282%2Aa%29+=+-%28%2B6%29%2F%282%2A1%29+=+-6%2F2+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer to your problem is h = -3<BR>\n" );
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document.write( "Here's the graph of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2+%2B+6x+-2 ALIGN=MIDDLE  ALT=\"y+=+x%5E2+%2B+6x+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (shown in red) to help you validate <BR>\n" );
document.write( "the answer. The green line is a vertical line through the vertex. It shows you that the<BR>\n" );
document.write( "vertex has -3 as the value for its x:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C5%2C-15%2C5%2Cx%5E2+%2B6x+-2%2C3000%28x%2B3%29%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C5%2C-15%2C5%2Cx%5E2+%2B6x+-2%2C3000%28x%2B3%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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