document.write( "Question 384777: identify the focus of 2x^2+5x+y+14=0 \n" ); document.write( "

Algebra.Com's Answer #280965 by lwsshak3(11628) $\"\"$ $\"About$

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identify the focus of 2x^2+5x+y+14=0
\n" ); document.write( "y=-2x^2-5x-14
\n" ); document.write( "factor out -2
\n" ); document.write( "then complete the square
\n" ); document.write( "y = -2(x^2+(5/2)x+25/16)-14+50/16
\n" ); document.write( "y = -2(x+5/4)^2-87/8
\n" ); document.write( "this is a parabola which opens downward whose vertex is at
\n" ); document.write( "(-5/4,-87/8)
\n" ); document.write( "y = -2(x+5/4)^2-87/8
\n" ); document.write( "-2(x+5/4)^2=y+87/8
\n" ); document.write( "(x+5/4)^2=-1/2(y+87/8)
\n" ); document.write( "this is now in form x^2 = 4py
\n" ); document.write( "4p=1/2
\n" ); document.write( "p=1/8
\n" ); document.write( "line of symmetry is at x=-5/4
\n" ); document.write( "focus is on the line of symmetry p units below the vertex=87/8-1/8=86/8=43/4\r
\n" ); document.write( "\n" ); document.write( "ans: the coordinates of the focus=(-5/4,-43/4)\r
\n" ); document.write( "\n" ); document.write( "see the following graph of the parabola\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-30%2C+10%2C-2x%5E2-5x-14%29+\"$ \n" ); document.write( "

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