document.write( "Question 112938: I need to take this equation from standard form to vertex form can someone please help me the problem is
\n" ); document.write( "x^2-18x+50 \n" ); document.write( "
Algebra.Com's Answer #82265 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%5E2-18+x%2B50\" Start with the given equation
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\n" ); document.write( " \"y-50=1+x%5E2-18+x\" Subtract \"50\" from both sides
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\n" ); document.write( " \"y-50=1%28x%5E2-18x%29\" Factor out the leading coefficient \"1\"
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\n" ); document.write( " Take half of the x coefficient \"-18\" to get \"-9\" (ie \"%281%2F2%29%28-18%29=-9\").
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\n" ); document.write( " Now square \"-9\" to get \"81\" (ie \"%28-9%29%5E2=%28-9%29%28-9%29=81\")
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\n" ); document.write( " \"y-50=1%28x%5E2-18x%2B81-81%29\" Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of \"81\" does not change the equation
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\n" ); document.write( " \"y-50=1%28%28x-9%29%5E2-81%29\" Now factor \"x%5E2-18x%2B81\" to get \"%28x-9%29%5E2\"
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\n" ); document.write( " \"y-50=1%28x-9%29%5E2-1%2881%29\" Distribute
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\n" ); document.write( " \"y-50=1%28x-9%29%5E2-81\" Multiply
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\n" ); document.write( " \"y=1%28x-9%29%5E2-81%2B50\" Now add \"50\" to both sides to isolate y
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\n" ); document.write( " \"y=1%28x-9%29%5E2-31\" 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=9\", and \"k=-31\". 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%5E2-18x%2B50\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1x%5E2-18x%2B50%29\" Graph of \"y=1x%5E2-18x%2B50\". Notice how the vertex is (\"9\",\"-31\").
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\n" ); document.write( " Notice if we graph the final equation \"y=1%28x-9%29%5E2-31\" we get:
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\n" ); document.write( " \"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C1%28x-9%29%5E2-31%29\" Graph of \"y=1%28x-9%29%5E2-31\". Notice how the vertex is also (\"9\",\"-31\").
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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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