document.write( "Question 803351: Identify the curve and find the center, directix, and focus. Then sketch the curve.\r
\n" ); document.write( "\n" ); document.write( " $\"%28y-2%29%5E2=%28x-3%29\"$ \r
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Algebra.Com's Answer #484301 by josgarithmetic(39617) $\"\"$ $\"About$

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A parabola comparable to $\"y%5E2=x\"$ , but the vertex is at (3,2). \r
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\n" ); document.write( "\n" ); document.write( " A standard derivation would typically be $\"y%5E2=4px\"$ in which p is the distance from vertex to directrix and from vertex to focus point. In your example, $\"4p=1\"$ , so $\"p=1%2F4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "To finish, center is (3,2), focus is at (3.25,2) and directrix at $\"x=2.75\"$ . The parabola opens toward the right.\r
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\n" ); document.write( "\n" ); document.write( "Graphing relies on finding two functions:
\n" ); document.write( " $\"y-2=0%2B-+sqrt%28x-3%29\"$
\n" ); document.write( " $\"y=2%2B-+sqrt%28x-3%29\"$
\n" ); document.write( " $\"highlight%28y=2-sqrt%28x-3%29%29\"$ and combine with $\"highlight%28y=2%2Bsqrt%28x-3%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28400%2C400%2C-12%2C12%2C-12%2C12%2C2-sqrt%28x-3%29%2C2%2Bsqrt%28x-3%29%29\"$ \n" ); document.write( "

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