document.write( "Question 41898This question is from textbook College Algebra Gary Rockswold
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\n" ); document.write( "\n" ); document.write( "a) Put the function in the form y = a(x - h)2 + k.
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\n" ); document.write( "\n" ); document.write( "b) What is the line of symmetry?
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\n" ); document.write( "\n" ); document.write( "c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x – h)2 + k.
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Algebra.Com's Answer #27019 by AnlytcPhil(1806) $\"\"$ $\"About$

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Quadratic_Equations/41898 (2006-06-12 22:24:03): \r\n" );
document.write( "Please, Please help me \r\n" );
document.write( "2) For the function y = x2 - 4x - 5, perform the following tasks: \r\n" );
document.write( "a) Put the function in the form y = a(x - h)2 + k.\r\n" );
document.write( "Answer: \r\n" );
document.write( "Show work in this space \r\n" );
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document.write( "y = 1x² - 4x - 5\r\n" );
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document.write( "1. Factor coefficient of x² out of first two terms, using brackets:\r\n" );
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document.write( "                       y = 1[x² - 4x] - 5\r\n" );
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document.write( "2. To the side, calculate the number requires to complete the square:\r\n" );
document.write( "     (I)  Multiply the coefficient of x by 1/2\r\n" );
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document.write( "         (-4)·(1/2) = -2 \r\n" );
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document.write( "    (II)  Square the result of (I)\r\n" );
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document.write( "         (-2)² = 4 \r\n" );
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document.write( "   (III)  Add this number and subtract it inside the brackets:\r\n" );
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document.write( "                      y = 1[x² - 4x + 4 - 4] - 5\r\n" );
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document.write( "3.  Inside the bracket, factor the trinomial consisting of the \r\n" );
document.write( "    first three terms, which should factor as a perfect square:\r\n" );
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document.write( "                      y = 1[(x - 2)(x - 2) - 4] - 5\r\n" );
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document.write( "                      y = 1[(x - 2)² - 4] - 5\r\n" );
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document.write( "4.  Remove the brackets, leaving the parentheses intact:\r\n" );
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document.write( "                      y = 1(x - 2)² - 4 - 5\r\n" );
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document.write( "5.  Combine the numbers\r\n" );
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document.write( "                      y = 1(x - 2)² - 9              \r\n" );
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document.write( "Compare to            y = a(x - h)² + k\r\n" );
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document.write( "                    So a = 1, h = 2, k = -9\r\n" );
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document.write( "b) What is the line of symmetry?\r\n" );
document.write( "Answer: \r\n" );
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document.write( "The axis of symmetry of the graph (parabola) whose equation is\r\n" );
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document.write( "                      y = a(x - h)² + k\r\n" );
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document.write( "is the vertical line whose equation is x = h\r\n" );
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document.write( "Therefore the axis of symmetry of\r\n" );
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document.write( "                      y = 1(x - 2)² - 9              \r\n" );
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document.write( "is the vertical line whose equation is x = 2\r\n" );
document.write( "                                  \r\n" );
document.write( "c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x – h)2 + k.\r\n" );
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document.write( "Explanation of graphing. \r\n" );
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document.write( "The vertex of the equation is                 \r\n" );
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document.write( "                         y = a(x - h)² + k\r\n" );
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document.write( "is the point (h, k)\r\n" );
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document.write( "So the vertex of the equation is                 \r\n" );
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document.write( "                         y = 1(x - 2)² - 9\r\n" );
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document.write( "is the point (2, -9)\r\n" );
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document.write( "Plot that point:\r\n" );
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document.write( "Two additional points are (h-1, k+a) and (h+1, k+a)\r\n" );
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document.write( "There are (2-1, -9+1) and (2+1, -9+1) or (1,-8) and (3,-8)\r\n" );
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document.write( "Plot those two points:\r\n" );
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document.write( "Draw a U-shaped curve through them:\r\n" );
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document.write( "d) In your own words, describe how this graph compares to the graph of y = x2? \r\n" );
document.write( "Answer:\r\n" );
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document.write( "The graph of y = x² is \r\n" );
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document.write( "It is shifted right h = 2 units (right) and k = -9 units (down)\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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