document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120176>Question 1120176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the quadratic function f(x) = 2x2– 8x + 11 <BR>\n" );
document.write( "Use “completing the squares” to convert the quadratic function into vertex form<BR>\n" );
document.write( "State the vertex, Find the x- and y-intercepts, Graph the function\r<BR>\n" );
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document.write( "the end answer is 2(x-2)^2 +3, I need the steps in-between the problem and the answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735841 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=735841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You might want to look at the lesson tutor @ikleyn suggested in her response.  Completing the square is a skill you might need in a lot of different types of math problems.<br><BR>\n" );
document.write( "In case they might help your understanding of the process, let me add a few notes of explanation to the solution as she showed it....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-8x%2B11 ALIGN=MIDDLE  ALT=\"2x%5E2-8x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Ignore the constant term for the moment; you need to complete the square in the variable x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2-8x%29%2B11 ALIGN=MIDDLE  ALT=\"%282x%5E2-8x%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To complete the square, you need to factor out the leading coefficient:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-4x%29%2B11 ALIGN=MIDDLE  ALT=\"2%28x%5E2-4x%29%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Think of the pattern for squaring a binomial: (x+a)^2 = x^2+2ax+a^2.  The coefficient of the middle term in the product is twice the constant term in the binomial.  So to complete a square you need to take half the coefficient of the linear term and square it.<br><BR>\n" );
document.write( "In this example, the coefficient of the linear term is -4; half of that squared is (-2)^2 = 4.  You need to complete the square in the parentheses by adding 4.<br><BR>\n" );
document.write( "Note that you have added 4 inside the parentheses, so you have added 2*4=8 to the expression as a whole.  To balance that, you need to subtract 8 from the expression (outside of the parentheses).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-4x%2B4%29%2B11-8 ALIGN=MIDDLE  ALT=\"2%28x%5E2-4x%2B4%29%2B11-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now write the trinomial as a binomial squared, and simplify the rest of the expression.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-2%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"2%28x-2%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The square of a number is always 0 or positive, so the minimum value of the expression will be when (x-2) is zero -- i.e., when x=2.  And the value of the expression when x=2 is 2(0^2)+3 = 3.  So the vertex of the graph is (2,3). </SPAN>\n" );
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