document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055220>Question 1055220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has one vertex on the line y = 8 – x (x > 0), another at the origin, one on the positive x-axis, and one on the positive y-axis. Express the area A of the rectangle as a function of x. Find the largest area A that can be enclosed by the rectangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670441 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=670441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A rectangle has one vertex on the line y = 8 – x (x > 0), another at the origin, one on the positive x-axis, <BR>\n" );
document.write( "and one on the positive y-axis. Express the area A of the rectangle as a function of x. <BR>\n" );
document.write( "Find the largest area A that can be enclosed by the rectangle.<BR>\n" );
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document.write( "1.  The area of a rectangle is  A = x*(8-x),  or  A = -x^2 + 8x.\r\n" );
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document.write( "    Simply because one dimension is x,  while the other dimension is  y = (8-x).\r\n" );
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document.write( "2.  The maximum of the quadratic function  A = -x^2 + 8x  is at\r\n" );
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document.write( "    x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2F%282%2A%28-1%29%29 ALIGN=MIDDLE  ALT=\"-8%2F%282%2A%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.\r\n" );
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document.write( "    Then  x = 4, y = 8-x = 4  and  A = 4*4 = 16 square units  is the maximal area.\r\n" );
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document.write( "See the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rectangle-with-the-given-perimeter-which-has-the-maximal-area-is-a-square.lesson>A rectangle with a given perimeter which has the maximal area is a square</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-garden-to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular garden to enclose the maximal area</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-area-along-the-river--to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular area along the river to enclose the maximal area</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rancher-planning-to-fence-two-adjacent-rectangular-corrals-to-enclose-the-maximal-area-.lesson>A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic \"<U>Finding minimum/maximum of quadratic functions</U>\". \r<BR>\n" );
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