document.write( "Question 689933: Use compliting square method to write the given quadratic equation \r
\n" ); document.write( "\n" ); document.write( "y=x^2-2x+3 as y=(x-h)^2+k. \n" ); document.write( "
Algebra.Com's Answer #426089 by MathLover1(20849)\"\" \"About 
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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%5E2-2+x%2B3\" Start with the given equation
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\n" ); document.write( " \"y-3=1+x%5E2-2+x\" Subtract \"3\" from both sides
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\n" ); document.write( " \"y-3=1%28x%5E2-2x%29\" Factor out the leading coefficient \"1\"
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\n" ); document.write( " Take half of the x coefficient \"-2\" to get \"-1\" (ie \"%281%2F2%29%28-2%29=-1\").
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\n" ); document.write( " Now square \"-1\" to get \"1\" (ie \"%28-1%29%5E2=%28-1%29%28-1%29=1\")
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\n" ); document.write( " \"y-3=1%28x%5E2-2x%2B1-1%29\" Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of \"1\" does not change the equation
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\n" ); document.write( " \"y-3=1%28%28x-1%29%5E2-1%29\" Now factor \"x%5E2-2x%2B1\" to get \"%28x-1%29%5E2\"
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\n" ); document.write( " \"y-3=1%28x-1%29%5E2-1%281%29\" Distribute
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\n" ); document.write( " \"y-3=1%28x-1%29%5E2-1\" Multiply
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\n" ); document.write( " \"y=1%28x-1%29%5E2-1%2B3\" Now add \"3\" to both sides to isolate y
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\n" ); document.write( " \"y=1%28x-1%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=1\", 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%5E2-2x%2B3\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2-2x%2B3%29\" Graph of \"y=1x%5E2-2x%2B3\". Notice how the vertex is (\"1\",\"2\").
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\n" ); document.write( " Notice if we graph the final equation \"y=1%28x-1%29%5E2%2B2\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x-1%29%5E2%2B2%29\" Graph of \"y=1%28x-1%29%5E2%2B2\". Notice how the vertex is also (\"1\",\"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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