document.write( "Question 615709: y=-(x+2)^2+2? \r
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Algebra.Com's Answer #387297 by Edwin McCravy(20065) $\"\"$ $\"About$
You can put this solution on YOUR website!
y = -(x + 2)² + 2
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document.write( "Learn the following:\r\n" );
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document.write( "y = A(x - H)² + K \r\n" );
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document.write( "is the equation of a curve called a parabola, that either looks like this\r\n" );
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document.write( " or like this: \r\n" );
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document.write( "If it looks like this , we say it OPENS UPWARD\r\n" );
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document.write( "If it looks like this , we say it OPENS DOWNWARD\r\n" );
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document.write( "The turning point (called the \"vertex\") is at the bottom of the graph\r\n" );
document.write( "if it looks like this  \r\n" );
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document.write( "The turning point or vertex is at the top of the graph if it looks \r\n" );
document.write( "like this .\r\n" );
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document.write( "The vertex is the point (H,K).\r\n" );
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document.write( "If A, the coefficient of the parentheses, is positive, the graph will\r\n" );
document.write( "look like this: \r\n" );
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document.write( "If A, the coefficient of the parentheses, is negative, the graph will\r\n" );
document.write( "look like this: .\r\n" );
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document.write( "Two points on each side of the vertex which the parabola goes through\r\n" );
document.write( "are (H-1,K+A) and (H+1,K+A)\r\n" );
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document.write( "Now let's compare your equation:\r\n" );
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document.write( "y = -(x + 2)² + 2\r\n" );
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document.write( "with this one:\r\n" );
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document.write( " y =  A(x - H)² + K\r\n" );
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document.write( "Put a 1 between the negative sign and the parentheses:\r\n" );
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document.write( " y = -1(x + 2)² + 2\r\n" );
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document.write( "You can see that A = -1, \r\n" );
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document.write( "You can see that -H = +2, and so H = -2\r\n" );
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document.write( "You can see that K = 2\r\n" );
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document.write( "Therefore the vertex (turning point) is (H,K) = (-2,2)\r\n" );
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document.write( "Since A is a negative number the parabola open downward and so it will\r\n" );
document.write( "look like this: \r\n" );
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document.write( "Two other points are (H-1,K+A) and (H+1,K+A).\r\n" );
document.write( "These are \r\n" );
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document.write( "(H-1,K+A) = (-2-1,2-1) = (-3,1) \r\n" );
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document.write( "and \r\n" );
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document.write( "(H+1,K+A = (-2+1,2-1) = (-1,1)\r\n" );
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document.write( "So we plot those three points, the vertex (-2,2), and the two points\r\n" );
document.write( "(-3,1) and (-1,1), like this::\r\n" );
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document.write( "Then we can sketch in the graph:\r\n" );
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document.write( "It has the axis of symmetry, which is a vertical line through the\r\n" );
document.write( "vertex, which has the equation \r\n" );
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document.write( "x = H\r\n" );
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document.write( " which in your case is the equation \r\n" );
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document.write( "x = -2, \r\n" );
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document.write( "and is the green vertical line below that goes through\r\n" );
document.write( "x = -2 on the x-axis:\r\n" );
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document.write( "Edwin
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