document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818813>Question 818813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express 3+9x-x^2 in the form of q-(x+r)^2,where q and r are constants.Hence<BR>\n" );
document.write( "(a)sketch it's extreme  value and the value of x when this occurs,<BR>\n" );
document.write( "(b)sketch the curve y=3+9x-x^2\r<BR>\n" );
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document.write( "I have found the values of q and r,but do not know what is extreme value and what does it mean.Please Help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492804 by </B><A HREF=/tutors/aboutme.mpl?userid=fcabanski><B>fcabanski(1391)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fcabanski><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=492804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The curve is a parabola.  The x-coordinate of the parabola's vertex (the extreme value other than the extremes at the end (+ or - infinity) is given by -b/2a where a is the coefficient 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;\" > term and b is the coefficient of the x term.<P><BR>\n" );
document.write( "For this equation a = -1 and b = 9 (c=3, but we won't use it until later).  -b/2a = -9/-2 = 9/2.<P><BR>\n" );
document.write( "Plug it back into the equation to find the y coordinate.<P><BR>\n" );
document.write( "3+9*9/2-81/4 = 93/4.  The vertex is (9/2,93/4).<P><BR>\n" );
document.write( "Find the x - intercepts, where the parabola crosses the x-axis, using the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-9+%2B-+sqrt%28+81%2B12+%29%29%2F%282%2A-1%29+ ALIGN=MIDDLE  ALT=\"%28-9+%2B-+sqrt%28+81%2B12+%29%29%2F%282%2A-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289+%2B-+sqrt%2893%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"%289+%2B-+sqrt%2893%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = approximately -.322 and 9.270.<P><BR>\n" );
document.write( "Plot the vertex and the intercepts.  Draw the curve. </SPAN>\n" );
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