document.write( "Question 1032404: how do I solve f(x)=-(x-3)^2 as a quadratic function? \n" ); document.write( "
Algebra.Com's Answer #647061 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Solving in this case means finding
\n" ); document.write( "the roots, or all \"+x+\" when \"+f%28x%29+=+0+\"
\n" ); document.write( "\"+0+=+-%28x-3%29%5E2+\"
\n" ); document.write( "I can see that \"+x=3+\" solves this
\n" ); document.write( "\"+0+=+-%28+3-3+%29%5E2+\"
\n" ); document.write( "\"+0+=+0+\"
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\n" ); document.write( "This is called a \"double root\" because a
\n" ); document.write( "quadratic should have 2 solutions
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\n" ); document.write( "The fact that there is one solution is shown by
\n" ); document.write( "both the graph and the quadratic formula:
\n" ); document.write( "\"+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "When there is just one solution, the discriminant is zero
\n" ); document.write( "\"+b%5E2+-+4a%2Ac+=+0+\"
\n" ); document.write( "---------------------
\n" ); document.write( "\"+f%28x%29+=+-%28x-3%29%5E2+\"
\n" ); document.write( "\"+f%28x%29+=+-%28+x%5E2+-+6x+%2B+9+%29+\"
\n" ); document.write( "\"+f%28x%29+=+-x%5E2+%2B+6x+-+9+\"
\n" ); document.write( "\"+a+=+1+\"
\n" ); document.write( "\"+b+=+6+\"
\n" ); document.write( "\"+c+=+-9+\"
\n" ); document.write( "----------------
\n" ); document.write( "The discriminant is:
\n" ); document.write( "\"+b%5E2+-+4a%2Ac+=+6%5E2+-+4%2A%28-1%29%2A%28-9%29+\"
\n" ); document.write( "\"+b%5E2+-+4a%2Ac+=+36+-+36+\"
\n" ); document.write( "\"+b%5E2+-+4a%2Ac+=+0+\"
\n" ); document.write( "------------------
\n" ); document.write( "So, referring to quadratic formula, the
\n" ); document.write( "single root is at:
\n" ); document.write( "\"+x+=+-b%2F%282a%29+\"
\n" ); document.write( "\"+x+=+-6%2F%282%2A%28-1%29%29+\"
\n" ); document.write( "\"+x+=+3+\" ( what we decided already )
\n" ); document.write( "--------------------
\n" ); document.write( "Here's the plot:
\n" ); document.write( "\"+graph%28+400%2C+400%2C+-2%2C+10%2C+-10%2C+2%2C+-x%5E2+%2B+6x+-+9+%29+\"\r
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