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find the vertex, and the line of symmetry, the maximum or minimum value of the quadratic function. then graph.
\n" ); document.write( "f(x)-2x^2+2x+8
\n" ); document.write( "x-vertex=
\n" ); document.write( "y-vetex=
\n" ); document.write( "line of symmetry=
\n" ); document.write( "max/min value=
\n" ); document.write( "is the value min or max=
\n" ); document.write( "..
\n" ); document.write( "Before I begin, I will assume a typing error in the given problem. After f(x) there should be an equal(=) sign instead of a minus (-) sign.
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\n" ); document.write( "\n" ); document.write( "The first step is to write equation to standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. An alternative method is to use the formula, -b/2a, to find the x-coordinate, then plugging it back into the equation to find the y-coordinate of the vertex. a is the coefficient of x^2, and b, is the coefficient of x. I will be doing the former method.
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\n" ); document.write( "\n" ); document.write( "f(x)=2x^2+2x+8
\n" ); document.write( "complete the square
\n" ); document.write( "y=2(x^2+x+1/4)+8-1/2
\n" ); document.write( "y=2(x+1/2)^2+15/2
\n" ); document.write( "This is shown to be a parabola opening upward with vertex at (-1/2,15/2)
\n" ); document.write( "The line of symmetry is a vertical line,x=-1/2. It has a minimum value=15/2\r
\n" ); document.write( "\n" ); document.write( "In summary:
\n" ); document.write( "vertex(-1/2,15/2)
\n" ); document.write( "line of symmetry x=-1/2
\n" ); document.write( "minimum value 15/2
\n" ); document.write( "The following is a graph of the parabola
\n" ); document.write( "..
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