document.write( "Question 1152314: Point P (u,v) is in the first quadrant on the graph of the line connecting the points (0,4) and (4,0). A shaded triangular region is shown in the diagram. For what point P will the area of the shaded triangular region be a maximum? \n" ); document.write( "

Algebra.Com's Answer #774308 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "x-coordinate of the point P is \"u\";\r\n" );
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document.write( "y--coordinate of the point P is \"v\".\r\n" );
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document.write( "These coordinates satisfy equation\r\n" );
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document.write( "    u + v = 4.\r\n" );
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document.write( "The area of the triangle is \r\n" );
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document.write( "    S =  =  =  = .\r\n" );
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document.write( "Thus the area \"S\" is the quadratic function of \"u\".\r\n" );
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document.write( "It achieves the maximum value at  u = \"  \" =  =  = 2.\r\n" );
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document.write( "The value of the maximum is  S =  =  =  = 2.\r\n" );
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document.write( "ANSWER.  The area of the triangle has the maximum at the point P = (2,2), and the value of the maximum is 2.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to expand your knowledge in this class of problem and if you want to feel a solid ground under your legs,\r
\n" ); document.write( "\n" ); document.write( "look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the minimum/maximum of a quadratic function\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO complete the square to find the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - Briefly on finding the vertex of a parabola\r
\n" ); document.write( "\n" ); document.write( "    - A rectangle with a given perimeter which has the maximal area is a square\r
\n" ); document.write( "\n" ); document.write( "    - A farmer planning to fence a rectangular garden to enclose the maximal area\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Finding minimum/maximum of quadratic functions\". \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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