document.write( "Question 443938: what is the vertex, focus, and directrix of y=1/3x^2-2x+6 \n" ); document.write( "

Algebra.Com's Answer #306157 by poliphob3.14(115) $\"\"$ $\"About$

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First we need to find the standard form of the parabola equation:\r
\n" ); document.write( "\n" ); document.write( " $\"3y=x%5E2-6x%2B18\"$ => $\"x%5E2-6x%2B9=3y-9\"$ => $\"%28x-3%29%5E2=3%28y-3%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "The final equation is the equation of parabola with vertex (3, 3).\r
\n" ); document.write( "\n" ); document.write( "Since 4c=3 we get c=3/4, and the focus is (3, 3+3/4) or (3, 15/4).\r
\n" ); document.write( "\n" ); document.write( "The directrix is y=3-3/4=9/4.\r
\n" ); document.write( "\n" ); document.write( " $\"graph%28600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29x%5E2-2x%2B6%29\"$ \n" ); document.write( "

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