document.write( "Question 856223: What is the vertex of the parabola given by the equation \"y=3x%5E2-48x%2B115\"?
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\n" ); document.write( "So far I have completed the square giving me: \"x%5E2-16x-192=y%2B115-576\". When I factored the equation I got: \"%28x-24%29%28x%2B8%29=y-461\". \n" ); document.write( "
Algebra.Com's Answer #515845 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
min{y = 3x^2-48 x+115} = -77 at x = 8
\n" ); document.write( "3 x^2-48 x+115
\n" ); document.write( "derivative
\n" ); document.write( "6x-48
\n" ); document.write( "x=8
\n" ); document.write( "3*8^2-48*8+115
\n" ); document.write( "3*64-48*8+115
\n" ); document.write( "192-384+115
\n" ); document.write( "y=-77\r
\n" ); document.write( "\n" ); document.write( "3x^2-48x=-115
\n" ); document.write( "x^2-16x=-115/3\r
\n" ); document.write( "\n" ); document.write( "x^2-16x+64=(192-115)/3
\n" ); document.write( " 3(x-8)^2-77=y
\n" ); document.write( "vertex 8,-77
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\n" ); document.write( "x = 8+sqrt(77/3)
\n" ); document.write( "x = 8-sqrt(77/3)\r
\n" ); document.write( "\n" ); document.write( "parabola
\n" ); document.write( "focus | (8, -923/12)=(8, -76.9167)
\n" ); document.write( "vertex | (8, -77)
\n" ); document.write( "semi-axis length | 1/12=0.0833333
\n" ); document.write( "focal parameter | 1/6=0.166667
\n" ); document.write( "eccentricity | 1
\n" ); document.write( "directrix | y = -925/12
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