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Complete the square as an aid to graphing :
\n" ); document.write( "y = -x^2 + 2x + 2
\n" ); document.write( ":
\n" ); document.write( "We want the coefficient of x^2 to be +1. Mult equation by -1 and you have:
\n" ); document.write( "x^2 - 2x - 2 = 0
\n" ); document.write( ":
\n" ); document.write( "Write it in the form for completing the square:
\n" ); document.write( ":
\n" ); document.write( "x^2 - 2x + __ = +2
\n" ); document.write( ":
\n" ); document.write( "Find the value that completes the square; divide the coefficient of x by 2, and
\n" ); document.write( "square it, here it's -2; -2/2 = -1 and -1^2 is +1, add 1 to both sides:
\n" ); document.write( ":
\n" ); document.write( "x^2 - 2x + 1 = 2 + 1
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\n" ); document.write( "x^2 - 2x + 1 = 3
\n" ); document.write( "or
\n" ); document.write( "(x-1)^2 = 3
\n" ); document.write( ":
\n" ); document.write( "Find the square root of both sides:
\n" ); document.write( "x - 1 = +/-Sqrt(3)
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\n" ); document.write( "x = 1 + Sqrt(3)
\n" ); document.write( "and
\n" ); document.write( "x = 1 - Sqrt(3)
\n" ); document.write( ":
\n" ); document.write( "These two values will be the x intercepts of your graph which looks like this:
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\n" ); document.write( "Note that 1 + Sqrt(3)is about +2.7 and 1 - Sqrt(3) is -.7, the x intercepts on
\n" ); document.write( "the above graph
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\n" ); document.write( "Did this help you understand this? \n" ); document.write( "