document.write( "Question 1071386: Form quadratic functions having the following properties:\r
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\n" ); document.write( "\n" ); document.write( "Zeroes at 1±sqrt(2), y-intercept at –4.\r
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\n" ); document.write( "\n" ); document.write( "(I tried the answers 4x^2-8x-4 and -4x^2-8x-4, but it didn't work)\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #686346 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given $\"f%28x%29=4x%5E2-8x-4\"$ as one of multiple choices,
\n" ); document.write( "you should find it works because
\n" ); document.write( "1) the y-intercept is $\"f%280%29=-4\"$ , and
\n" ); document.write( " $\"system%28f%28x%29=4x%5E2-8x-4%2Cf%28x%29=0%29\"$ --> $\"4x%5E2-8x-4=0\"$ --> $\"x%5E2-2x-1=0\"$ --> $\"x%5E2-2x=1\"$ --> $\"x%5E2-2x%2B1=1%2B1\"$ --> $\"%28x-1%29%5E2=2\"$ --> $\"x=1+%2B-+sqrt%282%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Given no multiple choice answers, you would have to find
\n" ); document.write( "function $\"f%28x%29\"$ yourself.
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\n" ); document.write( "ONE WAY TO DO IT:
\n" ); document.write( "With zeros at $\"1+%2B-+sqrt%282%29\"$ ,
\n" ); document.write( "the factored form of the quadratic function would be
\n" ); document.write( " $\"f%28x%29=a%28x-%281+%2B+sqrt%282%29%29%29%28x-%281+-+sqrt%282%29%29%29\"$
\n" ); document.write( "Simplifying and multiplying we get the standard $\"f%28x%29=ax%5E2%2Bbx%2Bc\"$ form.
\n" ); document.write( " $\"f%28x%29=a%28x-1+-+sqrt%282%29%29%28x-1+%2B+sqrt%282%29%29\"$
\n" ); document.write( " $\"f%28x%29=a%28%28x-1%29%5E2+-+%28sqrt%282%29%29%5E2%29\"$
\n" ); document.write( " $\"f%28x%29=a%28%28x%5E2-2x%2B1%29+-+2%29\"$
\n" ); document.write( " $\"f%28x%29=a%28x%5E2-2x%2B1+-+2%29\"$
\n" ); document.write( " $\"f%28x%29=a%28x%5E2-2x-1%29\"$
\n" ); document.write( " $\"f%28x%29=ax%5E2-2ax-a\"$
\n" ); document.write( "The y-intercept is
\n" ); document.write( " $\"system%28f%280%29=-4%2Cf%280%29=++-a%29\"$ , so $\"-4=-a\"$ --> $\"a=4\"$ ,
\n" ); document.write( "and $\"f%28x%29=4x%5E2-2%2A4x-4\"$ --> $\"f%28x%29=4x%5E2-8x-4\"$
\n" ); document.write( " $\"graph%28300%2C300%2C-1%2C3%2C-10%2C10%2C4x%5E2-8x-4%29\"$
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\n" ); document.write( "ANOTHER WAY:
\n" ); document.write( " $\"f%28x%29=ax%5E2%2Bbx%2Bc\"$ with $\"a%3C%3E0\"$ represents any and all quadratic functions.
\n" ); document.write( "If $\"-4\"$ is the y-intercept,
\n" ); document.write( " $\"system%28f%280%29=-4%2Cf%280%29=a%2Ao%5E2%2Bb%2A0%2Bc%29\"$ --> $\"system%28f%280%29=-4%2Cf%280%29=c%29\"$ --> $\"highlight%28c=-4%29\"$
\n" ); document.write( "The quadratic formula says that the zeros are given by
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\n" ); document.write( "If those zeros are
\n" ); document.write( " $\"x+=+1+%2B-+sqrt%282%29+\"$ , then setting the rational and irrational parts as equal,
\n" ); document.write( " $\"system%28%28-b%29%2F2a+=1%2C+sqrt%28+b%5E2-4%2Aa%2A%28-4%29%29%2Fabs%282a%29=sqrt%282%29%29\"$ --> $\"system%28b=-2a+%2C+%28b%5E2%2B16a%29%2F4a%5E2=2%29\"$ --> $\"system%28b=-2a%2C%284a%5E2%2B16a%29%2F4a%5E2=2%29\"$ --> $\"system%28b=-2a%2C4a%5E2%2B16a=2%2A4a%5E2%29\"$ --> $\"system%28b=-2a%2C4a%5E2%2B16a=8a%5E2%29\"$ --> $\"system%28b=-2a%2C16a=8a%5E2-4a%5E2%29\"$ --> $\"system%28b=-2a%2C16a=4a%5E2%29\"$ --> $\"system%28b=-2a%2C16=4a%29\"$ --> $\"system%28b=-2a%2C16%2F4=a%29\"$ --> $\"system%28b=-2a%2Ca=4%29\"$ --> $\"system%28b=-2%2A4%2Ca=4%29\"$ --> $\"highlight%28system%28b=-8%2Ca=4%29%29\"$ . \n" ); document.write( "

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