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What are the vertex, the axis of symmetry, the x any y intercepts and the domain and range of the following function? f(x)=2x^2-2x-4
\n" ); document.write( "***
\n" ); document.write( "y=2x^2-2x-4
\n" ); document.write( "complete the square
\n" ); document.write( "y=2(x^2-x+1/4)-4-1/2
\n" ); document.write( "y=2(x-1/2)^2-9/2
\n" ); document.write( "This is an equation of a parabola of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
\n" ); document.write( "For given equation:
\n" ); document.write( "lead coefficient>0 means parabola opens upwards and has a minimum
\n" ); document.write( "vertex:(1/2, -9/2)
\n" ); document.write( "axis of symmetry: x=1/2
\n" ); document.write( "..
\n" ); document.write( "y-intercept
\n" ); document.write( "set x=0
\n" ); document.write( "y=-4\r
\n" ); document.write( "\n" ); document.write( "x-intercept
\n" ); document.write( "set y=0
\n" ); document.write( "2(x-1/2)^2-9/2=0
\n" ); document.write( "2(x-1/2)^2=9/2
\n" ); document.write( "divide by 2
\n" ); document.write( "(x-1/2)^2=9/4
\n" ); document.write( "take sqrt of both sides
\n" ); document.write( "x-1/2=±3/2
\n" ); document.write( "x=1/2±3/2
\n" ); document.write( "x=2
\n" ); document.write( "or
\n" ); document.write( "x=-1
\n" ); document.write( "..
\n" ); document.write( "Domain: (-∞,∞)
\n" ); document.write( "Range: (-9/2,∞)
\n" ); document.write( "see graph below as a visual check on the answers:
\n" ); document.write( "