document.write( "Question 202334: Find the inverse of quadratic function, graph function and its inverse in the same coordinate plane.
\n" ); document.write( "y=x^2-2x+1\r
\n" ); document.write( "\n" ); document.write( "How do I find the answer? \n" ); document.write( "

Algebra.Com's Answer #152566 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find the inverse of the function:
\n" ); document.write( " $\"y+=+x%5E2-2x%2B1\"$ Exchange the x- and y-variables, then solve the resulting equation for y, thus:
\n" ); document.write( " $\"x+=+y%5E2-2y%2B1\"$ Solve this equation for y. Subtract X from both sides.
\n" ); document.write( " $\"y%5E2-2y%2B%281-x%29+=+0\"$ Use the quadratic formula to solve.
\n" ); document.write( " $\"y+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"$ In the equation just developed, a = 1, b = -2, and c = (1-x).
\n" ); document.write( " $\"y+=+%28-%28-2%2B-sqrt%28-2%29%5E2-4%281%29%281-x%29%29%29%2F2%281%29\"$ Simplify.
\n" ); document.write( " $\"y+=+%282%2B-sqrt%284-4%2B4x%29%29%2F2\"$
\n" ); document.write( " $\"y+=+%282%2F2%29%2Bsqrt%284x%29%2F2\"$ or $\"y+=+%282%2F2%29-sqrt%284x%29%2F2\"$ which can be further simplified into:
\n" ); document.write( " $\"highlight%28y%5E-1+=+1%2B-sqrt%28x%29%29\"$ This is the inverse.
\n" ); document.write( "In order to graph this, you must graph the two solutions as separate graphs:
\n" ); document.write( " $\"y+=+1%2Bsqrt%28x%29\"$ and $\"y+=+1-sqrt%28x%29\"$
\n" ); document.write( "The graph looks like:
\n" ); document.write( " $\"graph%28400%2C400%2C-5%2C10%2C-5%2C10%2Cx%5E2-2x%2B1%2C1%2Bsqrt%28x%29%2C1-sqrt%28x%29%29\"$
\n" ); document.write( "The red parabola is the graph of the given quadratic equation while the blue & green graphs combine to form the graph of the inverse funtion. \n" ); document.write( "

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