document.write( "Question 635035: y=|3x-6|+1\r
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Algebra.Com's Answer #400052 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "To draw the graph of the form: \r\n" );
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document.write( "y = a·|bx + c| + d\r\n" );
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document.write( "This is a graph shaped like this \"⋁\" or like this \"⋀\".\r\n" );
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document.write( "1.  Find the vertex (The sharp point of the graph) \r\n" );
document.write( "    A.  Set bx + c = 0 and solve for x.  This is the x-coordinate of the\r\n" );
document.write( "        vertex.\r\n" );
document.write( "    B.  The y-coordinate of the vertex is d.\r\n" );
document.write( "    C.  Plot this point.\r\n" );
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document.write( "2.  Find a point on the left of the vertex\r\n" );
document.write( "    A.  Select a value of x less than the x coordinate of the vertex\r\n" );
document.write( "        for the x-ccordinate of a second point on the graph. \r\n" );
document.write( "    B.   Substitute this value into the equation to find the corresponding\r\n" );
document.write( "        y-coordinate for that point.\r\n" );
document.write( "    C.  Plot that point.\r\n" );
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document.write( "3.  Find a point on the right of the vertex\r\n" );
document.write( "    A.  Select a value of x greater than the x coordinate of the vertex\r\n" );
document.write( "        for the x-ccordinate of a third point on the graph. \r\n" );
document.write( "    B.  Substitute this value into the equation to find the corresponding\r\n" );
document.write( "        y-coordinate for that point.\r\n" );
document.write( "    C.  Plot that point.\r\n" );
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document.write( "4. Draw a graph through those three points shaped like this \"⋁\" or like\r\n" );
document.write( "   this \"⋀\", with the vertex at the sharp point.\r\n" );
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document.write( "Let's go through your problem with those rules.\r\n" );
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document.write( "y =   |3x - 6| + 1\r\n" );
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document.write( "Compare to\r\n" );
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document.write( "y = a·|bx + c| + d\r\n" );
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document.write( "a=1, b=3, c=-6, d=1 \r\n" );
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document.write( "1.  Find the vertex (The sharp point of the graph) \r\n" );
document.write( "    A.  Set bx + c = 0 and solve for x.  \r\n" );
document.write( "            3x - 6 = 0 \r\n" );
document.write( "                3x = 6\r\n" );
document.write( "                 x = 2\r\n" );
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document.write( "    This is the x-coordinate of the vertex.\r\n" );
document.write( "    B.  The y-coordinate of the vertex is d=1.\r\n" );
document.write( "    C.  Plot this point, which is (2,1)\r\n" );
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document.write( "2.  Find a point on the left of the vertex\r\n" );
document.write( "    A.  Select a value of x less than the x coordinate of the vertex\r\n" );
document.write( "        for the x-ccordinate of a second point on the graph. \r\n" );
document.write( "     \r\n" );
document.write( "    Let's select 1 which is less than 2 \r\n" );
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document.write( "    B.   Substitute this value into the equation to find the corresponding\r\n" );
document.write( "         y-coordinate for that point.\r\n" );
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document.write( "         y = |3x - 6| + 1\r\n" );
document.write( "         y = |3(1) - 6| + 1 \r\n" );
document.write( "         y = |3 - 6| + 1\r\n" );
document.write( "         y = |-3| + 1\r\n" );
document.write( "         y = 3 + 1\r\n" );
document.write( "         y = 4, so the second point is (1,4)\r\n" );
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document.write( "    C.  Plot that point.\r\n" );
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document.write( "3.  Find a point on the right of the vertex\r\n" );
document.write( "    A.  Select a value of x greater than the x coordinate of the vertex\r\n" );
document.write( "        for the x-ccordinate of a third point on the graph. \r\n" );
document.write( "     \r\n" );
document.write( "    Let's select 3 which is greater than 2 \r\n" );
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document.write( "    B.   Substitute this value into the equation to find the corresponding\r\n" );
document.write( "         y-coordinate for that point.\r\n" );
document.write( "      \r\n" );
document.write( "         y = |3x - 6| + 1\r\n" );
document.write( "         y = |3(3) - 6| + 1 \r\n" );
document.write( "         y = |9 - 6| + 1\r\n" );
document.write( "         y = |3| + 1\r\n" );
document.write( "         y = 3 + 1\r\n" );
document.write( "         y = 4, so the third point is (3,4)\r\n" );
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document.write( "    C.  Plot that point.\r\n" );
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document.write( "4. Draw a graph through those three points shaped like this \"⋁\" or like\r\n" );
document.write( "   this \"⋀\", with the vertex at the sharp point.\r\n" );
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document.write( "   In this case it is shaped like this \"⋁\", so we draw in the graph: \r\n" );
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document.write( "Edwin
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