document.write( "Question 83166: 1) write an equation for the parabola whose vertex is at (-8,4) and passes through (-6,-2)\r
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Algebra.Com's Answer #59691 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "1) write an equation for the parabola whose \r\n" );
document.write( "vertex is at (-8,4) and passes through (-6,-2) \r\n" );
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document.write( "The equation of a parabola with vertex (h,k) is\r\n" );
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document.write( "    y = a(x - h)² + k\r\n" );
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document.write( "Substitute in (h,k) = (-8,4)\r\n" );
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document.write( "    y = a(x - (-8) )² + (4)\r\n" );
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document.write( "    y = a(x + 8)² + 4\r\n" );
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document.write( "Now we can substitute (x,y) = (-6,-2)\r\n" );
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document.write( " (-2) = a(-6 + 8)² + 4\r\n" );
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document.write( "   -2 = a(2)² + 4\r\n" );
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document.write( "   -2 = a(4) + 4\r\n" );
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document.write( "   -2 = 4a + 4\r\n" );
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document.write( "   -6 = 4a\r\n" );
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document.write( " \"-6%2F4\" = a \r\n" );
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document.write( " \"-3%2F2\" = a\r\n" );
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document.write( "So substitute \"-3%2F2\" for a in\r\n" );
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document.write( "    y = a(x + 8)² + 4\r\n" );
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document.write( "and we have\r\n" );
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document.write( "    y = \"-3%2F2\"(x + 8)² + 4\r\n" );
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document.write( "Drawing the graph:\r\n" );
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document.write( "2) i need to write: y = x² + 4x - 1 in vertex form \r\n" );
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document.write( "    y = x² + 4x - 1\r\n" );
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document.write( "factor 1 out of the first two terms on the right:\r\n" );
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document.write( "    y = 1(x² + 4x) - 1\r\n" );
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document.write( "Complete the square by \r\n" );
document.write( "1. taking 1/2 of the coefficient of x\r\n" );
document.write( "2. squaring that quantity\r\n" );
document.write( "3. Adding it and subtracting it inside the\r\n" );
document.write( "   parentheses.\r\n" );
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document.write( "1. 1/2 of 4 is 2\r\n" );
document.write( "2. 2 squared is 4\r\n" );
document.write( "3.\r\n" );
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document.write( "    y = 1(x² + 4x + 4 - 4) - 1\r\n" );
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document.write( "Change the parentheses to brackets:\r\n" );
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document.write( "    y = 1[x² + 4x + 4 - 4] - 1\r\n" );
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document.write( "Factor the frirst three terms inside the\r\n" );
document.write( "bracket:\r\n" );
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document.write( "    y = 1[(x + 2)(x + 2) - 4] - 1\r\n" );
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document.write( "Write (x + 2)(x + 2) as (x + 2)²\r\n" );
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document.write( "    y = 1[(x + 2)² - 4] - 1\r\n" );
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document.write( "Remove the bracket by distributing the 1\r\n" );
document.write( "into the bracket, leaving the parentheses\r\n" );
document.write( "intact.\r\n" );
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document.write( "    y = 1(x + 2)² - 4 - 1\r\n" );
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document.write( "Combine the last two terms\r\n" );
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document.write( "    y = 1(x + 2)² - 5\r\n" );
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document.write( "Copare that to\r\n" );
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document.write( "    y = a(x - h)² + k\r\n" );
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document.write( "and you can see that a = 1, h = -2, k = -5\r\n" );
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document.write( "so the vertex is (h,k) = (-2,-5) \r\n" );
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document.write( "3) which quadratic function has its vertex at (-2,7)\r\n" );
document.write( " and opens down?\r\n" );
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document.write( "Well, many many poarabolas have that vertex and\r\n" );
document.write( "open down.  We'll find one.\r\n" );
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document.write( "  Substitute (h,k) = (-2,7) in the standard equation\r\n" );
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document.write( "     y = a(x - h)² + k\r\n" );
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document.write( "     y = a(x - (-2) )² + 7\r\n" );
document.write( "     \r\n" );
document.write( "     y = a(x + 2)² + 7\r\n" );
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document.write( "But then choose any negative number for a, and its\r\n" );
document.write( "graph will open downward.  For instance, letting \r\n" );
document.write( "a = -1 gives this parabola:\r\n" );
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document.write( "    y = -(x + 2)² + 7\r\n" );
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document.write( "Edwin
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