document.write( "Question 86029: I need help with this homework question: Find the standard form of the function f(x)=x^2-4x+6. I do not understand this at all. \n" ); document.write( "
Algebra.Com's Answer #62148 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%5E2-4+x%2B6\" Start with the given equation
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\n" ); document.write( " \"y-6=1+x%5E2-4+x\" Subtract \"6\" from both sides
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\n" ); document.write( " \"y-6=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-6=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-6=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-6=1%28x-2%29%5E2-1%284%29\" Distribute
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\n" ); document.write( " \"y-6=1%28x-2%29%5E2-4\" Multiply
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\n" ); document.write( " \"y=1%28x-2%29%5E2-4%2B6\" Now add \"6\" to both sides to isolate y
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\n" ); document.write( " \"y=1%28x-2%29%5E2%2B2\" 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%5E2-4x%2B6\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2-4x%2B6%29\" Graph of \"y=1x%5E2-4x%2B6\". 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%2B2\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x-2%29%5E2%2B2%29\" Graph of \"y=1%28x-2%29%5E2%2B2\". 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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