document.write( "Question 541006: y=-(x^2)+4x-1 \n" ); document.write( "

Algebra.Com's Answer #354021 by jpg7n16(66) $\"\"$ $\"About$

You can put this solution on YOUR website!
Step 1: Factor out -1 to make the X side look normal
\n" ); document.write( " $\"y=%28-1%29%28x%5E2-4x%2B1%29\"$
\n" ); document.write( "Step 2: Factor the quadratic - which you can't do as is. You need to adjust it and make it workable. Although $\"X%5E2-4X%2B1\"$ isn't factorable, $\"X%5E2-4x%2B4\"$ is. So both add and subtract 4 from the right hand side, but don't reduce. Simultaneously adding and subtracting 4 is a net change of zero, so the equation will still balance.
\n" ); document.write( " $\"y=%28-1%29%28x%5E2-4x%2B4-4%2B1%29\"$
\n" ); document.write( "Step 3: Factor the quadratic, and reduce.
\n" ); document.write( " $\"x%5E2-4x%2B4=%28x-2%29%5E2\"$
\n" ); document.write( "So $\"y=%28-1%29%28x%5E2-4x%2B4-4%2B1%29\"$ becomes
\n" ); document.write( " $\"y=%28-1%29%28%28x-2%29%5E2-3%29\"$
\n" ); document.write( " $\"y=-%28x-2%29%5E2%2B3\"$
\n" ); document.write( "Step 4: Set y=0 and solve for x
\n" ); document.write( " $\"y=-%28x-2%29%5E2%2B3\"$
\n" ); document.write( " $\"0=-%28x-2%29%5E2%2B3\"$
\n" ); document.write( " $\"-3=-%28x-2%29%5E2\"$
\n" ); document.write( " $\"3=%28x-2%29%5E2\"$
\n" ); document.write( " $\"sqrt%283%29=x-2\"$ and $\"sqrt%283%29=-x%2B2\"$
\n" ); document.write( " $\"x=2%2B-sqrt%283%29\"$ \n" ); document.write( "

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