document.write( "Question 88269: Find the axis of symmetry.\r
\n" ); document.write( "\n" ); document.write( "y = –x^2 + 4x – 6
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Algebra.Com's Answer #64100 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: Completing the Square to Get a Quadratic into Vertex Form

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\n" ); document.write( " \"y=-1+x%5E2%2B4+x-6\" Start with the given equation
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\n" ); document.write( " \"y%2B6=-1+x%5E2%2B4+x\" Add \"6\" to both sides
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\n" ); document.write( " \"y%2B6=-1%28x%5E2-4x%29\" Factor out the leading coefficient \"-1\"
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\n" ); document.write( " Take half of the x coefficient \"-4\" to get \"-2\" (ie \"%281%2F2%29%28-4%29=-2\").
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\n" ); document.write( " Now square \"-2\" to get \"4\" (ie \"%28-2%29%5E2=%28-2%29%28-2%29=4\")
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\n" ); document.write( " \"y%2B6=-1%28x%5E2-4x%2B4-4%29\" Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of \"4\" does not change the equation
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\n" ); document.write( " \"y%2B6=-1%28%28x-2%29%5E2-4%29\" Now factor \"x%5E2-4x%2B4\" to get \"%28x-2%29%5E2\"
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\n" ); document.write( " \"y%2B6=-1%28x-2%29%5E2%2B1%284%29\" Distribute
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\n" ); document.write( " \"y%2B6=-1%28x-2%29%5E2%2B4\" Multiply
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\n" ); document.write( " \"y=-1%28x-2%29%5E2%2B4-6\" Now add \"%2B6\" to both sides to isolate y
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\n" ); document.write( " \"y=-1%28x-2%29%5E2-2\" Combine like terms
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\n" ); document.write( " Now the quadratic is in vertex form \"y=a%28x-h%29%5E2%2Bk\" where \"a=-1\", \"h=2\", and \"k=-2\". Remember (h,k) is the vertex and \"a\" is the stretch/compression factor.
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\n" ); document.write( " Check:
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\n" ); document.write( " Notice if we graph the original equation \"y=-1x%5E2%2B4x-6\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-1x%5E2%2B4x-6%29\" Graph of \"y=-1x%5E2%2B4x-6\". Notice how the vertex is (\"2\",\"-2\").
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\n" ); document.write( " Notice if we graph the final equation \"y=-1%28x-2%29%5E2-2\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-1%28x-2%29%5E2-2%29\" Graph of \"y=-1%28x-2%29%5E2-2\". Notice how the vertex is also (\"2\",\"-2\").
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\n" ); document.write( " So if these two equations were graphed on the same coordinate plane, one would overlap another perfectly. So this visually verifies our answer.
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