document.write( "Question 408680: What is the vertex, axis of symmetry, focus, and directrix of the parabola y^2=-8x \n" ); document.write( "

Algebra.Com's Answer #287817 by MathLover1(20849) $\"\"$ $\"About$

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What is the vertex, axis of symmetry, focus, and directrix of the parabola $\"y%5E2=-8x\"$ \r
\n" ); document.write( "\n" ); document.write( "since your parabola $\"y%5E2=-8x\"$ is y^2 = 4px in standard form, that is a parabola with vertex at origin\r
\n" ); document.write( "\n" ); document.write( "The vertex is (0 ,0)\r
\n" ); document.write( "\n" ); document.write( "Directrix is $\"x+=+-p\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-8x%2Fx=4px%2Fx\"$
\n" ); document.write( " $\"-8=4p\"$
\n" ); document.write( " $\"-8%2F4=p\"$
\n" ); document.write( " $\"-2=p\"$ \r
\n" ); document.write( "\n" ); document.write( "Focus is at (p, 0)..........(-2, 0)\r
\n" ); document.write( "\n" ); document.write( "Since the $\"x\"$ $\"+axis+\"$ is the axis of $\"symmetry\"$ of the parabola and its $\"vertex\"$ is at the origin, the equation of the parabola has the form\r
\n" ); document.write( "\n" ); document.write( " $\"y%5E2+=+4ax\"$ \r
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\n" ); document.write( "\n" ); document.write( "The point (-2 , 4) lies on the parabola: $\"4%5E2+=4a%28-2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Solve for a: a = -2 ; the equation is: $\"y%5E2+=+-8x\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2Csqrt%28-8x%29%2C+-sqrt%28-8x%29%29+\"$ \r
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