document.write( "Question 118862: What are the procedures to write a quadratic equation in vertex form? \n" ); document.write( "
Algebra.Com's Answer #86979 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
What are the procedures to write a quadratic equation in vertex form?
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document.write( "First of all, learn what the vertex form is,\r\n" );
document.write( "and how to graph the parabola from that form:\r\n" );
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document.write( "The vertex form of \r\n" );
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document.write( "y = a(x - h)² + k\r\n" );
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document.write( "has vertex (h, k) and goes through the two points,\r\n" );
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document.write( "(h-1,k+a) and (h+1,k+a) \r\n" );
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document.write( "Example 1:\r\n" );
document.write( "Suppose you started with\r\n" );
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document.write( "y = 2x² - 12x + 22\r\n" );
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document.write( "1. Factor the coefficient of x² out of the first\r\n" );
document.write( "   two terms, using a bracket, so you can put\r\n" );
document.write( "   parentheses inside of it: \r\n" );
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document.write( "   y = 2[x² - 6x] + 22\r\n" );
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document.write( "2. Out to the side or on scratch paper, complete\r\n" );
document.write( "   the square by:\r\n" );
document.write( "   (a) Multiplying the coefficient of x by \"1%2F2\".\r\n" );
document.write( "        -6(\"1%2F2\") = -3    \r\n" );
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document.write( "   (b) Squaring the result of (a).\r\n" );
document.write( "        (-3)² = +9\r\n" );
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document.write( "3.  Add, then subtract, the result of 2.(b) inside\r\n" );
document.write( "    the brackets:\r\n" );
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document.write( "    y = 2[x² - 6x + 9 - 9] + 22\r\n" );
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document.write( "4. Factor the binomial consisting of the first three\r\n" );
document.write( "   terms inside the brackets:\r\n" );
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document.write( "    y = 2[(x - 3)(x - 3) - 9] + 22\r\n" );
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document.write( "5. If everything has gone right, the two factors of \r\n" );
document.write( "   that binomial will be the same, making it a \r\n" );
document.write( "   perfect square, so write it as a binomial squared:\r\n" );
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document.write( "   y = 2[(x - 3)² - 9] + 22\r\n" );
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document.write( "6. Remove the brackets by distributing, remembering\r\n" );
document.write( "   to leave the parentheses intact:\r\n" );
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document.write( "   y = 2(x - 3)² - 18 + 22\r\n" );
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document.write( "7. Combine the last two numerical terms:\r\n" );
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document.write( "   y = 2(x - 3)² + 4\r\n" );
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document.write( "Compare that to\r\n" );
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document.write( "   y = a(x - h)² + k\r\n" );
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document.write( "Then a = 2, h = 3 and k = 4. So by the\r\n" );
document.write( "above, the graph has vertex (h, k) = (3,4) and \r\n" );
document.write( "it goes through the two points,\r\n" );
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document.write( "(h-1,k+a) = (3-1,4+3) = (2,7)\r\n" );
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document.write( "and\r\n" );
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document.write( "(h+1,k+a) = (3+1,4+3) = (4,7)\r\n" );
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document.write( "So plot those three points:\r\n" );
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document.write( "and draw a U-shaped graph through them, called a parabola:\r\n" );
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document.write( "  \r\n" );
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document.write( "Example 2:\r\n" );
document.write( "Suppose you started with\r\n" );
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document.write( "y = -x² - 8x - 13\r\n" );
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document.write( "y = -(x + 4)² + 3\r\n" );
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document.write( "1. Factor the coefficient of x² out of the first\r\n" );
document.write( "   two terms, using a bracket, so you can put\r\n" );
document.write( "   parentheses inside of it: \r\n" );
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document.write( "   y = -1[x² + 8x] - 13\r\n" );
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document.write( "2. Out to the side or on scratch paper, complete\r\n" );
document.write( "   the square by:\r\n" );
document.write( "   (a) Multiplying the coefficient of x by \"1%2F2\".\r\n" );
document.write( "         8(\"1%2F2\") = +4    \r\n" );
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document.write( "   (b) Squaring the result of (a).\r\n" );
document.write( "        (+4)² = +16\r\n" );
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document.write( "3.  Add, then subtract, the result of 2.(b) inside\r\n" );
document.write( "    the brackets:\r\n" );
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document.write( "    y = -1[x² + 8x + 16 - 16] - 13\r\n" );
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document.write( "4. Factor the binomial consisting of the first three\r\n" );
document.write( "   terms inside the brackets:\r\n" );
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document.write( "    y = -1[(x + 4)(x + 4) - 16] - 13\r\n" );
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document.write( "5. If everything has gone right, the two factors of \r\n" );
document.write( "   that binomial will be the same, making it a \r\n" );
document.write( "   perfect square, so write it as a binomial squared:\r\n" );
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document.write( "   y = -1[(x + 4)² - 16] - 13\r\n" );
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document.write( "6. Remove the brackets by distributing, remembering\r\n" );
document.write( "   to leave the parentheses intact:\r\n" );
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document.write( "   y = -1(x + 4)² + 16 - 13\r\n" );
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document.write( "7. Combine the last two numerical terms:\r\n" );
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document.write( "   y = -1(x + 4)² + 3\r\n" );
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document.write( "Compare that to\r\n" );
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document.write( "   y = a(x - h)² + k\r\n" );
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document.write( "Then a = -1, h = -4 and k = 3. So by the\r\n" );
document.write( "above, the graph has vertex (h, k) = (-4,3) and \r\n" );
document.write( "it goes through the two points,\r\n" );
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document.write( "(h-1,k+a) = ( -4-1, 3+(-1) ) = (-5,2)\r\n" );
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document.write( "and\r\n" );
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document.write( "(h+1,k+a) = ( -4+1, 3+(-1) ) = (-3,2)\r\n" );
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document.write( "So plot those three points:\r\n" );
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document.write( "and draw a U-shaped graph through them, called a parabola. This is\r\n" );
document.write( "an upside down U graph which will always be the case whenever \"a\",\r\n" );
document.write( "the coefficient of x² is a negative number:\r\n" );
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document.write( "  \r\n" );
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document.write( "Edwin
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